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Kuznetsov, Dmitriy Feliksovich

Total publications: 139 (129)
in MathSciNet: 48 (47)
in zbMATH: 68 (68)
in Web of Science: 42 (42)
in Scopus: 37 (36)
Cited articles: 16
Citations: 74
Presentations: 2

Number of views:
This page:32088
Abstract pages:3047
Full texts:636
References:255
Kuznetsov, Dmitriy Feliksovich
Doctor of physico-mathematical sciences (2003)
Speciality: 05.13.18 (Mathematical modelling, calculating methods, and the program systems)
Birth date: 24.04.1970
E-mail:
Website: http://www.sde-kuznetsov.spb.ru
Keywords: iterated Ito stochastic integral, iterated Stratonovich stochastic integral, Wiener process, multidimensional Wiener process, infinite-dimensional $Q$-Wiener process, Ito stochastic differential equation, stochastic differential equation of jump-diffusion type, non-commutative semilinear stochastic partial differential equation with nonlinear multiplicative trace class noise, stochastic Ito-Taylor expansion, stochastic Stratonovich-Taylor expansion, generalized multiple Fourier series, multiple Fourier-Legendre series, multiple trigonometric Fourier series, mean-square approximation of iterated stochastic integrals, approximation with probability $1$ of iterated stochastic integrals, high-order strong numerical methods for Ito stochastic differential equations, numerical modeling of stochastic systems.
UDC: 519.2, 519.21, 519.6, 517.521, 517.521.5, 517.586, 519.85
MSC: 60H10, 60H35, 65C30, 60H05, 42B05, 42C10

Subject:

Fourier method for numerical integration of Ito stochastic differential equations (SDEs)$,$ SDEs of jump-diffusion type as well as for non-commutative semilinear stochastic partial differential equations (SPDEs) with nonlinear multiplicative trace class noise (within the framework of a semigroup approach or an approach based on the so-called mild solution) has been proposed and developed$.$ More precisely$,$ the generalized multiple Fourier series (converging in the sense of norm in Hilbert space $L_2([t,\hspace{0.2mm} T]^k),$ $k\in \mathbb {N}$) in arbitrary complete orthonormal systems of functions in the space $L_2([t,\hspace{0.2mm} T]^k),$ $k\in \mathbb {N}$ have been applied to expansion and strong approximation (mean-square approximation$,$ approximation in the mean of degree $p$ $(p>0)$ as well as approximation with probability $1$) of iterated Ito stochastic integrals of the form \begin{equation} \label{1} \int\limits_t^T\psi_k(t_k)\ \ldots \int\limits_t^{t_{2}} \psi_1(t_1) d{\bf W}_{t_1}^{(i_1)}~ \ldots~ d{\bf W}_{t_k}^{(i_k)}, \end{equation} where $k\in \mathbb {N},\ $ $\psi_{1}(\tau),\ldots,\psi_k(\tau)\in L_2[t, T],\ $ ${\bf W}_{\tau} \in \mathbb{R^m}$ is a standard multidimensional Wiener process with independent components ${\bf W}_{\tau}^{(i)}$ $(i=1,\ldots,m)\ $ and $\ {\bf W}_{\tau}^{(0)}:=\tau,\ $ $i_1,\ldots,i_k$ $=0,\ 1,\ldots,m.$

The relationship of the mentioned expansion with the multiple Wiener stochastic integrals with respect to components of a multidimensional Wiener process and Hermite polynomials of the vector random argument is established. The mean-square approximation error for iterated Ito stochastic integrals of form $(1)$ of arbitrary multiplicity $k,\ $ $k\in\mathbb{N}$ for all possible combinations of indices $i_1,\ldots, i_k \in\{1,\ldots, m\}$ in the framework of this approach has been calculated exactly.

Theorem on convergence with probability $1$ for expansions of iterated Ito stochastic integrals $(1)$ of arbitrary multiplicity $k\in\mathbb{N}$ has been fomulated and proved for the case of multiple Fourier-Legendre series and multiple trigonometric Fourier series converging in the sense of norm in the space $L_2([t,\hspace{0.2mm} T]^k),$ $k\in \mathbb {N}$ as well as for $\psi_{1}(\tau),\ldots,\psi_k(\tau)\in C^1[t,T].$ The rate of convergence in this theorem is found.

Generalizations of the Fourier method for complete orthonormal with weight $r(t_1) \ldots r(t_k)$ systems of functions in the space $L_2([t,\hspace{0.2mm} T]^k),$ $k\in \mathbb {N}$ as well as for some other types of iterated stochastic integrals (iterated stochastic integrals with respect to martingale Poisson measures and iterated stochastic integrals with respect to martingales) were obtained$.$

The above results were adapted under a special condition on trace series for iterated Stratonovich stochastic integrals of the form \begin{equation} \label{2} \int\limits_t^T\psi_k(t_k)\ \ldots \int\limits_t^{t_{2}} \psi_1(t_1)\hspace{0.3mm} \circ d{\bf W}_{t_1}^{(i_1)}\ \ldots\hspace{0.5mm} \circ d{\bf W}_{t_k}^{(i_k)}, \end{equation} where $k\in \mathbb {N},\ $ $\psi_{1}(\tau),\ldots,\psi_k(\tau)\in L_2[t,T],\ $ ${\bf W}_{\tau} \in \mathbb{R^m}$ is a standard multidimensional Wiener process with independent components ${\bf W}_{\tau}^{(i)}$ $(i=1,\ldots,m)\ $ and $\ {\bf W}_{\tau}^{(0)}:=\tau,\ $ $i_1,\ldots,i_k$ $=0,\ 1,\ldots,m.$ The above condition on trace series was removed for the following three cases.

$1.$ The case of multiple Fourier series in complete orthonormal systems of Legendre polynomials and trigonometric functions (Fourier basis) in $L_2([t,\hspace{0.2mm} T]^k)$ as well as $\psi_1(\tau),\ldots,\psi_k(\tau)\in C^1[t,T]$ $(k=1,\ldots,5),$ $\psi_1(\tau),\ldots,\psi_6(\tau)\equiv 1$ $(k=6).$ The rate of mean-square convergence of expansions of iterated Stratonovich stochastic integrals is found for this case $(k=1,\ldots,5).$

$2.$ The case of multiple Fourier series in arbitrary complete orthonormal systems in $L_2([t,T]^k)$ and $\psi_1(\tau), \psi_2(\tau)\in L_2[t,T]$ $(k=1, 2),$ $\psi_1(\tau),\ldots, \psi_k(\tau)\in C[t, T]$ $(k=3,\ 4,\ 5).$

$3.$ The case of multiple Fourier series in arbitrary complete orthonormal systems in $L_2([t,T]^k)$ and $\psi_1(\tau), \ldots, \psi_k(\tau)$ $\in$ $C[t, T]\ $ $(k\in\mathbb{N})$ (https://arxiv.org/pdf/2003.14184v57, Sect. 2.31, Theorem 2.61).

These results can be interpreted as Wong-Zakai type theorems on the convergence of iterated Riemann-Stieltjes integrals to iterated Stratonovich stochastic integrals. The hypothesis on expansion of iterated Stratonovich stochastic integrals of form $(2)$ has been formulated for the case of an arbitrary multiplicity $k\in \mathbb {N}.$

We formulated and proved two theorems on expansion of iterated Stratonovich stochastic integrals of form $(2)$ of arbitrary multiplicity $k\in \mathbb {N}$ based on iterated Fourier series converging pointwise.

Numerical simulation of iterated Ito and Stratonovich stochastic integrals $(1)$ and $(2)$ is one of the main problems at the stage of numerical realization of high-order strong numerical methods for Ito SDEs and SDEs of jump-diffusion type$.$

Fourier method for iterated Ito stochastic integrals $(1)$ is also applied to the mean-square approximation of iterated stochastic integrals with respect to the infinite-dimensional $Q$-Wiener process$.$ In particular$,$ to the mean-square approximation of integrals of the form $$ \int\limits_{t}^{T} \Psi_k(Z) \left( \ldots \left(\hspace{0.2mm} \int\limits_{t}^{t_2} \Psi_1(Z) \psi_1(t_1) d{\bf W}_{t_1}({\bf x})\right) \ldots \right) \psi_k(t_k) d{\bf W}_{t_k}({\bf x}), $$ where $k\in \mathbb {N},\hspace{0.2mm}$ ${\bf W}_{\tau}({\bf x})$ is an $U$-$\hspace{0.2mm}$valued $Q\hspace{0.2mm}$-$\hspace{0.2mm}$Wiener process$,$ $Z:$ $\Omega \rightarrow H$ is an ${\bf F}_t/{\cal B}(H)\hspace{0.2mm}$-$\hspace{0.2mm}$measurable mapping$,$ $\Psi_k(v) (\hspace{0.5mm} \ldots ( \Psi_1(v) ) \ldots )$ is a $k~$-$\hspace{0.2mm}$linear Hilbert-Schmidt operator mapping from $U_0\times\ldots \times U_0$ to $H$ for all $v\in H,~$ $\psi_1(\tau),\ldots,\psi_k(\tau)\in L_2[t,T],\ $ $Q:~U \rightarrow U$ is a trace class operator$,$ $\hspace{0.2mm}$ $U,$ $H$ are separable real-valued Hilbert spaces$,\ $ $U_0=Q^{1/2}U.$

Mean-square approximation of iterated stochastic integrals with respect to the infinite-dimensional $Q$-Wiener process is one of the most difficult problems in numerical implementation of high-order strong approximation schemes (with respect to the temporal discretization) for non-commutative semilinear SPDEs with nonlinear multiplicative trace class noise (approximation schemes based on the so-called mild solution)$.$

Legende polynomials were first applied to the mean-square approximation of iterated Ito and Stratonovich stochastic integrals $(1)$ and $(2)$ with multiplicities $1$ to $6.$ It is shown that the Legendre polynomial system is the optimal system for solving this problem for $k\ge 3.$

Theorems on replacing the order of integration for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales were formulated and proved$.$

The so-called unified Ito-Taylor and Stratonovich-Taylor expansions were derived$.$

Strong numerical methods of high-orders of accuracy $\gamma =1.0,$ $1.5,$ $2.0,$ $2.5,$ $3.0, ... $ for Ito SDEs with multidimensional and non-commutative noise were constructed$.$ Among them there are explicit and implicit$,$ one-step and multistep methods as well as the methods of Runge-Kutta type$.$

His research interests also include various types of stochastic integrals and their properties as well as the numerical modeling of linear and nonlinear stochastic dynamical systems$.$

Biography

In 1993 he graduated from Department of Mechanics and Control Processes of Faculty of Physics and Mechanics of Saint-Petersburg State Technical University (Peter the Great Saint-Petersburg Polytechnic University). Ph.D. (1996), doctor of phisico-mathematical sciences (2003), professor of Department of Mathematics of Peter the Great Saint-Petersburg Polytechnic University since 2006, author of monographs on numerical integration of Ito stochastic differential equations and strong approximation of iterated Ito and Stratonovich stochastic integrals.

   
Main publications:
  1. Kuznetsov D. F., Kuznetsov M. D., “Mean-square approximation of iterated stochastic integrals from strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear SPDEs based on multiple Fourier-Legendre series”, Recent Developments in Stochastic Methods and Applications, ICSM-5 2020, Springer Proceedings in Mathematics & Statistics, 371, eds. Shiryaev A.N., Samouylov K.E, Kozyrev D.V., Springer, Cham, 2021, 17–32  crossref  mathscinet  elib  scopus
  2. Kuznetsov D. F., “Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor–Stratonovich expansion”, "Computational Mathematics and Mathematical Physics", 60:3 (2020), 379–389  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  3. Kuznetsov D. F., “A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations”, "Computational Mathematics and Mathematical Physics", 59:8 (2019), 1236–1250  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  4. Kuznetsov D. F., “Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations”, "Computational Mathematics and Mathematical Physics", 58:7 (2018), 1058–1070  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  5. Kuznetsov D. F., “Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs”, 2024, 1–1152, arXiv: 2003.14184  crossref  adsnasa  isi  elib

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https://arxiv.org/a/kuznetsov_d_1

Full list of publications:
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Citations (Crossref Cited-By Service + Math-Net.Ru)
1. Dmitriy F. Kuznetsov, Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals, The 4th International Conference on Stochastic Methods (ICSM-4), June 2–9, 2019, Divnomorskoe, Russia, Presentation PDF
2. Dmitriy F. Kuznetsov, Application of multiple Fourier–Legendre series to the implementation of strong exponential Milstein and Wagner–Platen methods for non-commutative semilinear SPDEs, The 5th International Conference On Stochastic Methods (ICSM-5), November 23-27, 2020, Moscow, Russia, Presentation PDF
3. Dmitriy F. Kuznetsov., A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process., ICSM-7, 2-9 June, 2022, Divnomorskoe, Presentation PDF
4. Dmitriy F. Kuznetsov., Recent results on a new approach to the series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process, ICSM-8, 2-8 June, 2023, Divnomorskoe, Presentation PDF
5. Dmitriy F. Kuznetsov, New results on expansion of iterated Itô and Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process. The case of arbitrary CONS in $L_2[t, T]$, ICSM-9, 2-8 June, 2024, Divnomorskoe, Presentation PDF

   2024
6. Dmitriy F. Kuznetsov, Expansions of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series: multiplicities 1 to 6 and beyond, 2024 (Published online) , 355 pp., arXiv: 1712.09516  crossref  zmath  adsnasa  isi  elib
7. Dmitriy F. Kuznetsov, The hypotheses on expansions of iterated Stratonovich stochastic integrals of arbitrary multiplicity and their partial proof, 2024 (Published online) , 281 pp., arXiv: 1801.03195  crossref  zmath  adsnasa  isi  elib
8. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of fifth and sixth multiplicity based on generalized multiple Fourier series, 2024 (Published online) , 270 pp., arXiv: 1802.00643  crossref  zmath  adsnasa  isi  elib
9. Dmitriy F. Kuznetsov, Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs, 2024 (Published online) , 1152 pp., arXiv: 2003.14184  crossref  adsnasa  isi  elib
10. Dmitriy F. Kuznetsov, “A new approach to the series expansion of iterated Stratonovich stochastic integrals with respect to components of the multidimensional Wiener process. The case of arbitrary complete orthonormal systems in Hilbert space”, Electronic Journal “Differential Equations and Control Processes”, 2024, no. 2, 73–170 Publication Page  PDF  crossref  mathscinet  zmath  scopus
11. Dmitriy F. Kuznetsov, “A new approach to the series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process. The case of arbitrary complete orthonormal systems in Hilbert space. II”, Electronic Journal “Differential Equations and Control Processes”, 2024, no. 4, 104–178 (to appear)  crossref
12. D. F. Kuznetsov, “Expansions of iterated Itô and Stratonovich stochastic integrals. The case of arbitrary CONS in $L_2[t, T ]$”, 9th International Conference on Stochastic Methods (ICSM-9) (Divnomorskoe, Russia, June 2–8, 2024), Theory of Probability and its Applications, 69, no. 4, 2024 (to appear)

   2023
13. Dmitriy F. Kuznetsov, Expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series converging in the mean, 2023 (Published online) , 144 pp., arXiv: 1712.09746  crossref  zmath  adsnasa  isi  elib
14. Dmitriy F. Kuznetsov, “Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Integration of Ito SDEs and Semilinear SPDEs (Third Edition)”, Electronic Journal “Differential Equations and Control Processes”, 2023, no. 1, A.1-A.947 Publication Page  PDF  crossref  mathscinet  zmath  elib  scopus 2
15. D. F. Kuznetsov, “Recent results on a new approach to series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of a multidimensional Wiener process”, 8th International Conference on Stochastic Methods (ICSM-8) (Divnomorskoe, Russia, June 1–8, 2023), Theory of Probability and its Applications, 68, no. 4, 2023, 688–688 PDF  crossref  isi 1
16. Dmitriy F. Kuznetsov, “A new proof of the series expansion of iterated Itô stochastic integrals with respect to the components of a multidimensional Wiener process based on generalized multiple Fourier series and Hermite polynomials”, Electronic Journal “Differential Equations and Control Processes”, 2023, no. 4, 67-124 Publication Page  PDF  crossref  mathscinet  zmath  elib  scopus
17. Dmitriy F. Kuznetsov, A new proof of the expansion of iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process based on generalized multiple Fourier series and Hermite polynomials, 2023 (Published online) , 58 pp., arXiv: 2307.11006  crossref  zmath  adsnasa  isi

   2022
18. Dmitriy F. Kuznetsov, New Theory of the Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Integration of Ito SDEs and semilinear SPDEs, 28 arXiv.org articles, 2022 (Published online) , 2131 pp. PDF  elib
19. Dmitriy F. Kuznetsov, “A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process”, Electronic Journal “Differential Equations and Control Processes”, 2022, no. 2, 83–186 Publication Page  PDF  mathscinet  zmath  elib  scopus

   2023
20. D. F. Kuznetsov, “A new approach to series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of a multidimensional Wiener process”, 7th International Conference on Stochastic Methods (ICSM-7) (Divnomorskoe, Russia, June 2–9, 2022), Theory of Probability and its Applications, 67, no. 4, 2023, 665–666 PDF  crossref  crossref  isi  elib

   2022
21. Dmitriy F. Kuznetsov, “A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process. II”, Electronic Journal “Differential Equations and Control Processes”, 2022, no. 4, 135–194 Publication Page  PDF  mathscinet  zmath  elib  scopus
22. Kuznetsov D. F., Kuznetsov M. D., “Optimization of the mean-square approximation procedures for iterated Stratonovich stochastic integrals of multiplicities 1 to 3 with respect to components of the multi-dimensional Wiener process based on Multiple Fourier–Legendre series”, MATEC Web of Conferences, 362 (2022), article id: 01014 , 10 pp. PDF  crossref  isi

   2021
23. Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, “SDE–MATH: A software package for the implementation of strong high-order numerical methods for Ito SDEs with multidimensional non-commutative noise based on multiple Fourier–Legendre series”, Electronic Journal “Differential Equations and Control Processes”, 2021, no. 1, 93-422 Publication Page  PDF  mathscinet  zmath  elib  scopus
24. Kuznetsov D. F., Kuznetsov M. D., “Mean-square approximation of iterated stochastic integrals from strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear SPDEs based on multiple Fourier-Legendre series”, In: Recent Developments in Stochastic Methods and Applications. ICSM-5 2020, Springer Proceedings in Mathematics & Statistics, ISBN 978-3-030-83266-7, 371, eds. Shiryaev A.N., Samouylov K.E, Kozyrev D.V., Springer, Cham, 2021, 17–32 Publication Page  crossref  mathscinet  elib  scopus
25. Kuznetsov D. F., Kuznetsov M. D., “Optimization of the mean-square approximation procedures for iterated Ito stochastic integrals based on multiple Fourier-Legendre series”, Journal of Physics: Conference Series, 1925 (2021), article id: 012010 , 12 pp. PDF  crossref  isi  elib  scopus 1
26. Kuznetsov D. F., “Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Integration of Ito SDEs and Semilinear SPDEs. 2nd Edition”, Electronic Journal “Differential Equations and Control Processes”, 2021, no. 4, A.1–A.788 Publication Page  PDF  mathscinet  zmath  elib  scopus
27. Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Software Package, Gosudarstvennaya registratsiya programmy dlya EVM (RU2021616047), 2021 PDF  elib
28. Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Fourier-Legendre Coefficients Database, Gosudarstvennaya registratsiya bazy dannykh, okhranyaemoi avtorskimi pravami (RU2021620788), 2021 PDF  elib

   2020
29. D. F. Kuznetsov, “Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor–Stratonovich expansion”, Computational Mathematics and Mathematical Physics, 60:3 (2020), 379–389  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
30. D. F. Kuznetsov, “Strong approximation of iterated Ito and Stratonovich stochastic integrals”, 4th International Conference on Stochastic Methods (ICSM-4) (Divnomorskoe, Russia, June 2–9, 2019), Theory of Probability and its Applications, 65, no. 1, 2020, 141–142 PDF  mathnet  mathnet  crossref  crossref  mathscinet  isi  elib  elib
31. Dmitriy F. Kuznetsov, Four new forms of the Taylor-Ito and Taylor-Stratonovich expansions and its application to the high-order strong numerical methods for Ito stochastic differential equations, 2020 (Published online) , 90 pp., arXiv: 2001.10192  crossref  zmath  adsnasa  isi  elib
32. Dmitriy F. Kuznetsov, “The proof of convergence with probability 1 in the method of expansion of iterated Ito stochastic integrals based on generalized multiple Fourier series”, Electronic Journal "Differential Equations and Control Processes, 2020, no. 2, 89–117 Publication Page  PDF  mathscinet  zmath  elib  scopus
33. Dmitriy F. Kuznetsov, “Application of multiple Fourier–Legendre series to implementation of strong exponential Milstein and Wagner–Platen methods for non-commutative semilinear stochastic partial differential equations”, Electronic Journal "Differential Equations and Control Processes, 2020, no. 3, 129–162 Publication Page  PDF  mathscinet  zmath  elib  scopus
34. Dmitriy F. Kuznetsov, “Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals Based on Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs. 1st Edition”, Electronic Journal “Differential Equations and Control Processes”, 2020, no. 4, A.1–A.606 Publication Page  PDF  mathscinet  zmath  elib  scopus
35. Dmitriy F. Kuznetsov, “Application of multiple Fourier–Legendre series to the implementation of strong exponential Milstein and Wagner–Platen methods for non-commutative semilinear SPDEs”, Proceedings of the XIII International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI-2020). (6-13 September, 2020, Alushta, Crimea), MAI, Moskva, 2020, 451–453 PDF  elib
36. Dmitriy F. Kuznetsov, The proof of convergence with probability 1 in the method of expansion of iterated Ito stochastic integrals based on generalized multiple Fourier series, 2020 , 33 pp., arXiv: 2006.16040  crossref  adsnasa  isi
37. Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, Implementation of strong numerical methods of orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito SDEs with non-commutative noise based on the unified Taylor-Ito and Taylor-Stratonovich expansions and multiple Fourier-Legendre series, 2020 , 343 pp., arXiv: 2009.14011  crossref  zmath  adsnasa  isi  elib
38. Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, Optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 5 from the unified Taylor-Ito expansion based on multiple Fourier-Legendre series., 2020 , 63 pp., arXiv: 2010.13564  crossref  zmath  adsnasa  elib
39. Kuznetsov D.F., Kuznetsov M.D., “A software package for Implementation of strong numerical methods of convergence orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito SDEs with non-commutative multi-dimensional noise”, 19th International Conference “Aviation and Cosmonautics” (AviaSpace-2020). Abstracts (Moscow, MAI, 23-27 November, 2020), Publishing house “Pero”, 2020, 569–570 PDF  elib
40. Dmitriy F. Kuznetsov, “Application of multiple Fourier-Legendre series to the implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear SPDEs with nonlinear multiplicative trace class noise”, The 5th International Conference on Stochastic Methods (ICSM-5). Proceedings (Russia, Moscow, November 23–27, 2020), RUDN Press, 2020, 88–92 PDF  elib

   2019
41. D. F. Kuznetsov, “On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence”, Automation and Remote Control, 80:5 (2019), 867–881  mathnet  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
42. D. F. Kuznetsov, “Expansion of iterated Stratonovich stochastic integrals, based on generalized multiple Fourier series”, Ufa Mathematical Journal, 11:4 (2019), 49–77 PDF  mathnet  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
43. Dmitriy F. Kuznetsov, Comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations, 2019 (Published online) , 40 pp., arXiv: 1901.02345  crossref  adsnasa  isi  elib
44. D. F. Kuznetsov, “A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations”, Computational Mathematics and Mathematical Physics, 59:8 (2019), 1236–1250  mathnet  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
45. Dmitriy F. Kuznetsov, Application of the method of approximation of iterated stochastic Ito integrals based on generalized multiple Fourier series to the high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations, 2019 (Published online) , 41 pp., arXiv: 1905.03724  crossref  adsnasa  isi  elib
46. Dmitriy F. Kuznetsov, “Application of the Fourier method for the numerical solution of stochastic differential equations”, 2nd International Conference on Mathematical Modeling in Applied Sciences. Book of Abstracts. (Belgorod, Russia, August 20–24, 2019), 2019, 236–237 PDF  elib
47. Dmitriy F. Kuznetsov, “Application of the method of approximation of iterated stochastic Ito integrals based on generalized multiple Fourier series to the high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations”, Electronic Journal "Differential Equations and Control Processes, 2019, no. 3, 18–62 (Published online) Publication Page  PDF  mathscinet  zmath  elib  scopus
48. Dmitriy F. Kuznetsov, New simple method of expansion of iterated Ito stochastic integrals of multiplicity 2 based on expansion of the Brownian motion using Legendre polynomials and trigonometric functions, 2019 (Published online) , 23 pp., arXiv: 1807.00409  crossref  zmath  adsnasa  isi  elib
49. D. F. Kuznetsov, “Approksimatsiya povtornykh stokhasticheskikh integralov Ito vtoroi kratnosti, osnovannaya na razlozhenii vinerovskogo protsessa s pomoschyu mnogochlenov Lezhandra i trigonometricheskikh funktsii”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 2019, no. 4, 32–52 Publication Page  PDF  mathscinet  zmath  elib  scopus
50. Dmitriy F. Kuznetsov, Application of multiple Fourier–Legendre series to implementation of strong exponential Milstein and Wagner–Platen methods for non-commutative semilinear stochastic partial differential equations, 2019 , 32 pp., arXiv: 1912.02612  crossref  adsnasa  isi  elib

   2018
51. Dmitriy F. Kuznetsov, Exact calculation of the mean-square error in the method of approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series, 2018 (Published online) , 71 pp., arXiv: 1801.01079  crossref  zmath  adsnasa  isi  elib
52. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity based on generalized iterated Fourier series converging pointwise, 2018 (Published online) , 80 pp., arXiv: 1801.00784  crossref  zmath  adsnasa  isi  elib
53. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of multiplicity 3 based on generalized multiple Fourier series converging in the mean: general case of series summation, 2018 (Published online) , 66 pp., arXiv: 1801.01564  crossref  zmath  adsnasa  isi  elib
54. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of multiplicity 2 based on double Fourier-Legendre series summarized by Pringsheim method, 2018 (Published online) , 49 pp., arXiv: 1801.01962  crossref  zmath  adsnasa  isi  elib
55. Dmitriy F. Kuznetsov, Integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales, 2018 (Published online) , 28 pp., arXiv: 1801.04634  crossref  zmath  adsnasa  elib
56. Dmitriy F. Kuznetsov, Expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4. Combained approach based on generalized multiple and iterated Fourier series, 2018 (Published online) , 46 pp., arXiv: 1801.05654  crossref  zmath  adsnasa  isi  elib
57. Dmitriy F. Kuznetsov, Expansion of iterated stochastic integrals with respect to martingale Poisson measures and with respect to martingales based on generalized multiple Fourier series, 2018 (Published online) , 40 pp., arXiv: 1801.06501  crossref  zmath  adsnasa  isi  elib
58. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of multiplicity 2. Combined approach based on generalized multiple and iterated Fourier series, 2018 (Published online) , 20 pp., arXiv: 1801.07248  crossref  zmath  adsnasa  isi  elib
59. Dmitriy F. Kuznetsov, Expansions of iterated Stratonovich stochastic integrals from the Taylor-Stratonovich expansion based on multiple trigonometric Fourier series. Comparison with the Milstein expansion, 2018 (Published online) , 36 pp., arXiv: 1801.08862  crossref  zmath  adsnasa  isi  elib
60. D. F. Kuznetsov, “Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations”, Computational Mathematics and Mathematical Physics, 58:7 (2018), 1058–1070  mathnet  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
61. Dmitriy F. Kuznetsov, To numerical modeling with strong orders 1.0, 1.5, and 2.0 of convergence for multidimensional dynamical systems with random disturbances, 2018 (Published online) , 29 pp., arXiv: 1802.00888  crossref  adsnasa  elib
62. Dmitriy F. Kuznetsov, Explicit one-step strong numerical methods of orders 2.0 and 2.5 for Ito stochastic differential equations based on the unified Taylor-Ito and Taylor-Stratonovich expansions, 2018 (Published online) , 37 pp., arXiv: 1802.04844  crossref  zmath  adsnasa  isi  elib
63. D. F. Kuznetsov, “Razlozhenie povtornykh stokhasticheskikh integralov Stratonovicha vtoroi kratnosti, osnovannoe na dvoinykh ryadakh Fure-Lezhandra, summiruemykh po Prinskheimu”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 2018, no. 1, 1–34 (Published online) Publication Page  PDF  mathscinet  zmath  elib
64. D. F. Kuznetsov, “On numerical modeling of the multidimensional dynamic systems under random perturbations with the 1.5 and 2.0 orders of strong convergence”, Automation and Remote Control, 79:7 (2018), 1240–1254  mathnet  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
65. Dmitriy F. Kuznetsov, Numerical simulation of 2.5-set of iterated Ito stochastic integrals of multiplicities 1 to 5 from the Taylor-Ito expansion, 2018 (Published online) , 29 pp., arXiv: 1805.12527  crossref  zmath  adsnasa  isi  elib
66. Dmitriy F. Kuznetsov, Numerical simulation of 2.5-set of iterated Stratonovich stochastic integrals of multiplicities 1 to 5 from the Taylor-Stratonovich expansion, 2018 (Published online) , 29 pp., arXiv: 1806.10705  crossref  adsnasa  elib
67. Dmitriy F. Kuznetsov, Strong numerical methods of orders 2.0, 2.5, and 3.0 for Ito stochastic differential equations based on the unified stochastic Taylor expansions and multiple Fourier-Legendre series, 2018 (Published online) , 44 pp., arXiv: 1807.02190  crossref  zmath  adsnasa  isi  elib
68. D. F. Kuznetsov, “Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. S programmami v srede MATLAB (6-e izdanie)”, Elektronnyi zhurnal “Differentsialnye uravneniya i protsessy upravleniya”, 2018, no. 4, A.1–A.1073 (Published online) Publication Page  PDF, dopolnitelnaya ssylka: PDF  mathscinet  zmath  elib

   2017
69. Dmitriy F. Kuznetsov, “Strong approximation of multiple Ito and Stratonovich stochastic integrals”, International Conference on Mathematical Modeling in Applied Sciences. Abstracts Book (St.-Petersburg, Russia, July 24–28, 2017), Polytechnic University Publishing House, 2017, 141–142 PDF  elib
70. Dmitriy F. Kuznetsov, Development and application of the Fourier method to the mean-square approximation of iterated Ito and Stratonovich stochastic integrals, 2017 (Published online) , 58 pp., arXiv: 1712.08991  crossref  adsnasa  isi  elib
71. Dmitriy F. Kuznetsov, Mean-square approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 from the Taylor-Ito and Taylor-Stratonovich expansions using Legendre polynomials, 2017 (Published online) , 106 pp., arXiv: 1801.00231  crossref  zmath  adsnasa  isi  elib
72. D. F. Kuznetsov, “Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. S programmami v srede MATLAB (5-e izdanie)”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 2017, no. 2, A.1–A.1000 (Published online) Publication Page  PDF  crossref  mathscinet  zmath  elib
73. Dmitriy F. Kuznetsov, “Multiple Ito and Stratonovich Stochastic Integrals: Fourier-Legendre and Trigonometric Expansions, Approximations, Formulas”, Electronic Journal "Differential Equations and Control Processes, 2017, no. 1, A.1–A.385 (Published online) Publication Page  PDF  crossref  mathscinet  zmath  elib

   2013
74. Dmitriy F. Kuznetsov, Multiple Ito and Stratonovich Stochastic Integrals: Approximations, Properties, Formulas, Polytechnical University Publishing House, S.-Petersburg, 2013 , 382 pp., ISBN 978-5-7422-3973-4 PDF  crossref  zmath  elib

   2012
75. Dmitrii Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii Ito. S programmami v srede MatLab, Lambert Academic Publishing, Saarbrucken, 2012 , 692 pp., ISBN 978-3-8484-8214-6  zmath
76. Dmitriy F. Kuznetsov, Approximation of Multiple Ito and Stratonovich Stochastic Integrals. Multiple Fourier Series Approach, Lambert Academic Publishing, Saarbrücken, 2012 , 409 pp., ISBN 978-3-8484-3855-6 PDF  zmath

   2011
77. Dmitriy F. Kuznetsov, Strong Approximation of Multiple Ito and Stratonovich Stochastic Integrals: Multiple Fourier Series Approach. 2nd edition, Polytechnical University Publishing House, St.-Petersburg, 2011 , 284 pp., ISBN 978-5-7422-3162-2 PDF  crossref  zmath  elib
78. Dmitriy F. Kuznetsov, Strong Approximation of Multiple Ito and Stratonovich Stochastic Integrals: Multiple Fourier Series Approach. 1st edition, Polytechnical University Publishing House, St.-Petersburg, 2011 , 250 pp., ISBN 978-5-7422-2988-9 PDF  crossref  mathscinet  zmath  elib

   2010
79. D. F. Kuznetsov, Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. S programmami v srede MatLab. 4-e izdanie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2010 , XXX+786 pp., ISBN 978-5-7422-2448-8 PDF  crossref  mathscinet  zmath  elib
80. D. F. Kuznetsov, “Povtornye stokhasticheskie integraly Ito i Stratonovicha i kratnye ryady Fure”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 2010, no. 3, A.1–A.257 (Published online) Publication Page  PDF  crossref  mathscinet  zmath  elib

   2009
81. D. F. Kuznetsov, Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. S programmami v srede MatLab. 3-e izdanie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2009 , XXXIV+768 pp., ISBN 978-5-7422-2132-6 PDF  crossref  mathscinet  zmath  elib

   2008
82. D. F. Kuznetsov, “Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 2008, no. 1, A.1–A.29 (Published online) Publication Page  PDF  zmath  elib

   2007
83. D. F. Kuznetsov, Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. S programmami v srede MatLab. 2-e izdanie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2007 , XXXII+770 pp., ISBN 5-7422-1439-1 PDF  crossref  mathscinet  zmath  elib
84. D. F. Kuznetsov, Stokhasticheskie differentsialnye uravneniya: teoriya i praktika chislennogo resheniya. 1-e izdanie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2007 , 778 pp., ISBN 5-7422-1394-8 PDF  crossref  zmath  elib

   2006
85. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii. 2, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2006 , 764 pp., ISBN 5-7422-1191-0 PDF  crossref  zmath  elib
86. D. F. Kuznetsov, Matematika. Teoriya funktsii kompleksnoi peremennoi, Uchebnoe posobie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2006 , 124 pp.  elib

   2002
87. Kuznetsov D. F, “The three-step strong numerical methods of the orders of accuracy 1.0 and 1.5 for Ito stochastic differential equations”, Journal of Automation and Information Sciences (Begell House), 2002, 34 (Issue 12), 14 pp. PDF  crossref  mathscinet  isi  elib  elib  scopus  scopus
88. Kuznetsov D. F, “Combined method of strong approximation of multiple stochastic integrals”, Journal of Automation and Information Sciences (Begell House), 2002, 34 (Issue 8), 6 pp. PDF  crossref  mathscinet  isi  elib  elib  scopus  scopus
89. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, diss. … dokt. fiz.-matem. nauk, S.-Peterburg, 2002 , 490 pp.  elib
90. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, Avtoreferat diss. … dokt. fiz.-matem. nauk, Izdatelstvo SPbGTU, S.-Peterburg, 2002 , 34 pp.  elib

   2003
91. D. F. Kuznetsov, “New representations of the Taylor–Stratonovich expansion”, Journal of Mathematical Sciences (New York), 118:6 (2003), 5586–5596 PDF  mathnet  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

   2001
92. D. F. Kuznetsov, “New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations”, Computational Mathematics and Mathematical Physics, 41:6 (2001), 874–888 PDF  mathnet  mathnet  mathscinet  zmath  elib  elib  scopus
93. Kuznetsov D. F, “Finite-difference strong numerical methods of order 1.5 and 2.0 for stochastic differential Ito equations with nonadditive multidimensional noise”, Journal of Automation and Information Sciences (Begell House), 2001, 33 (Issue 5–8), 13 pp. PDF  crossref  mathscinet  isi  elib  elib  scopus  scopus
94. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, Izdatelstvo S.-Peterburgskogo gosudarstvennogo universiteta, S.-Peterburg, 2001 , 712 pp., ISBN: 5-288-02462-6  zmath  elib
95. D. F. Kuznetsov, “Correction to: D. F. Kuznetsov “New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations””, Computational Mathematics and Mathematical Physics, 41:12 (2001), 1816 PDF  mathnet  mathnet  crossref  mathscinet  elib  elib  scopus

   2000
96. Kuznetsov D. F, “Mean square approximation of solutions of stochastic differential equations using Legendres polynomials”, Journal of Automation and Information Sciences (Begell House), 2000, 32 (Issue 12), 69–86 PDF  crossref  mathscinet  mathscinet  elib  elib  scopus  scopus
97. D. F. Kuznetsov, “Slabyi chislennyi metod poryadka 4.0 dlya stokhasticheskikh differentsialnykh uravnenii Ito”, Vestnik molodykh uchenykh. Seriya “Prikladnaya matematika i mekhanika”, 2000, no. 4, 47–52 PDF  elib

   2002
98. D. F. Kuznetsov, “Expansion of the Stratonovich multiple stochastic integrals based on the Fourier multiple series”, Journal of Mathematical Sciences (New York), 109:6 (2002), 2148–2165 PDF  mathnet  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

   1999
99. Kuznetsov D. F, “Application of approximation methods of iterated Stratonovich and Ito stochastic integrals to numerical simulation of controlled stochastic systems”, Journal of Automation and Information Sciences (Begell House), 1999, 31 (Issue 10), 70–83  crossref  mathscinet  elib  elib  scopus
100. D. F. Kuznetsov, “K probleme chislennogo modelirovaniya stokhasticheskikh sistem”, Vestnik molodykh uchenykh. Seriya “Prikladnaya matematika i mekhanika”, 1999, no. 1, 20–32  elib
101. D. F. Kuznetsov, Chislennoe modelirovanie stokhasticheskikh differentsialnykh uravnenii i stokhasticheskikh integralov, Nauka, S.-Peterburg, 1999 , 460 pp., ISBN 5-02-024905-x  zmath  elib
102. D. F. Kuznetsov, Dva novykh predstavleniya razlozheniya Teilora-Stratonovicha, Preprint, Izdatelstvo SPbGTU, S.-Peterburg, 1999 , 13 pp. PDF  crossref  elib
103. D. F. Kuznetsov, Zamena poryadka integrirovaniya v povtornykh stokhasticheskikh integralakh po martingalu, Preprint, Izdatelstvo SPbGTU, S.-Peterburg, 1999 , 11 pp. PDF  crossref  elib
104. D. F. Kuznetsov, Primenenie polinomov Lezhandra k silnoi approksimatsii reshenii stokhasticheskikh differentsialnykh uravnenii, Preprint, Izdatelstvo SPbGTU, S.-Peterburg, 1999 , 17 pp. PDF  crossref  elib

   1998
105. D. F. Kuznetsov, “Nekotorye voprosy teorii chislennogo resheniya stokhasticheskikh differentsialnykh uranenii Ito”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1998, no. 1, 66–367 (Published online) Publication Page  PDF  crossref  mathscinet  zmath  elib
106. D. F. Kuznetsov, Nekotorye voprosy teorii chislennogo resheniya stokhasticheskikh differentsialnykh uravnenii Ito, Izdatelstvo SPbGTU, S.-Peterburg, 1998 , 204 pp., ISBN 5-7422-0045-5  mathscinet  zmath  elib
107. O. Yu. Kulchitskii, D. F. Kuznetsov, “Chislennoe modelirovanie reshenii stokhasticheskikh sistem lineinykh statsionarnykh differentsialnykh uravnenii”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1998, no. 1, 41–65 (Published online) Publication Page  PDF  mathscinet  zmath  elib
108. D. F. Kuznetsov, “Analiticheskie formuly dlya vychisleniya stokhasticheskikh integralov”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1998, no. 4, 18–28 Publication Page  PDF  mathscinet  zmath  elib
109. D. F. Kuznetsov, “Metod razlozheniya i approksimatsii povtornykh stokhasticheskikh integralov Stratonovicha, osnovannyi na kratnykh ryadakh Fure po polnym ortonormirovannym sistemam funktsii i ego primenenie k chislennomu resheniyu stokhasticheskikh differentsialnykh uravnenii Ito”, Proceedings of the International Workshop “Tools for Mathematical Modelling” (St.-Petersburg, 3–6 December, 1997), Izdatelstvo SPbGTU, S.-Peterburg, 1998, 135–160  mathscinet  elib

   1999
110. Kulchitskiy O. Yu., Kuznetsov D. F., “Numerical methods of modeling control systems described by stochastic differential equations”, Journal of Automation and Information Sciences (Begell House), 1999, 31 (Issues 1-3), 47–61  crossref  mathscinet  isi  elib  elib  scopus  scopus

   1998
111. Dmitriy F. Kuznetsov, “Method of expansion and approximation of repeated stochastic Stratonovich integrals, which is based on multiple Fourier series on full orthonormal systems”, Abstracts of communications. International Conference “Asymptotic Methods in Probability and Mathematical Statistics” dedicated to the 50-th anniversary of the chair of probability and statistics in St. Petersburg University (St.-Petersburg, 24–28 June, 1998), 1998, 146–149  elib
112. D. F. Kuznetsov, “Ispolzovanie razlichnykh polnykh ortonormirovannykh sistem funktsii dlya chislennogo resheniya stokhasticheskikh differentsialnykh uravnenii Ito”, The 2nd International Scientific and Practical Conference “Differential Equations and Applications”, Abstracts (St.-Petersburg, June 15–20, 1998), Izdatelstvo SPbGTU, S.-Peterburg, 1998, 128–129  elib
113. D. F. Kuznetsov, “Metod razlozheniya i approksimatsii povtornykh stokhasticheskikh integralov Stratonovicha, osnovannyi na kratnykh ryadakh Fure po polnym ortonormirovannym sistemam funktsii”, The 2nd International Scientific and Practical Conference “Differential Equations and Applications”, Abstracts (St.-Petersburg, June 15–20, 1998), Izdatelstvo SPbGTU, S.-Peterburg, 1998, 130–131  elib
114. Oleg Yu. Kulchitski, Dmitriy F. Kuznetsov, “Analitical formulas for calculating of stochastic integrals”, Abstracts of communications. International Conference “Asymptotic Methods in Probability and Mathematical Statistics” dedicated to the 50-th anniversary of the chair of probability and statistics in St. Petersburg University (St.-Petersburg, 24–28 June, 1998), 1998, 140–145  elib

   2000
115. O. Yu. Kulchitski, D. F. Kuznetsov, “The unified Taylor-Ito expansion”, Journal of Mathematical Sciences (New York), 99:2 (2000), 1130–1140 PDF  mathnet  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

   1997
116. D. F. Kuznetsov, “Metod razlozheniya i approksimatsii povtornykh stokhasticheskikh integralov Stratonovicha, osnovannyi na kratnykh ryadakh Fure po polnym ortonormirovannym sistemam funktsii”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1997, no. 1, 18–77 (Published online) Publication Page  PDF  mathscinet  zmath  elib
117. D. F. Kuznetsov, Teoremy o zamene poryadka integrirovaniya v povtornykh stokhasticheskikh integralakh, Dep. v VINITI, 3607-B97, 1997 , 31 pp.  elib
118. O. Yu. Kulchitskii, D. F. Kuznetsov, “Unifitsirovannoe razlozhenie Teilora - Ito”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1997, no. 1, 1–17 (Published online) Publication Page  PDF  mathscinet  zmath  elib
119. Kulchitskiy O. Yu., Kuznetsov D. F., “Numerical simulation of nonlinear oscillatory systems under stochastic perturbations”, Proceedings of the 1st International Conference “Control of Oscillations and Chaos” COC97 (St.-Petersburg, 27–29 August, 1997), Vol. 2, eds. F.L. Chernousko, A.L. Fradkov, 1997, 242–245  crossref  isi  elib  scopus
120. O. Yu. Kulchitsky, D. F. Kuznetsov, “Numerical simulation of stochastic control systems”, Proceedings of the International Conference on Informatics and Control ICI&C97 (St.-Petersburg, 9–13 June, 1997), Vol. 1, Published by St.-Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences (SPIIRAS), 1997, 368–376  elib
121. D. F. Kuznetsov, Teoreticheskoe obosnovanie metoda razlozheniya i approksimatsii povtornykh stokhasticheskikh integralov Stratonovicha, osnovannogo na kratnykh ryadakh Fure po trigonometricheskim i sfericheskim funktsiyam, Dep. v VINITI. 3608-V97, 1997 , 27 pp.  elib
122. O. Yu. Kulchitskii, D. F. Kuznetsov, “Biblioteka programm stokhasticheskogo modelirovaniya lineinykh upravlyaemykh sistem v srede MATLAB”, Mezhdunarodnaya konferentsiya “Sredstva matematicheskogo modelirovaniya” (S.-Peterburg, 3–6 dekabrya, 1997), Izdatelstvo SPbGTU, S.-Peterburg, 1997, 97–98  elib

   1996
123. D. F. Kuznetsov, Metody chislennogo modelirovaniya reshenii sistem stokhasticheskikh differentsialnykh uravnenii Ito v zadachakh mekhaniki, Avtoreferat diss. … kand. fiz.-matem. nauk, Izdatelstvo SPbGTU, S.-Peterburg, 1996 , 19 pp.  elib
124. D. F. Kuznetsov, Konechno-raznostnyi metod chislennogo integrirovaniya stokhasticheskikh differentsialnykh uravnenii Ito s lokalnoi srednekvadraticheskoi oshibkoi tretego poryadka malosti, Dep. v VINITI. 3510-B96, 1996 , 27 pp.  elib
125. D. F. Kuznetsov, Konechno-raznostnaya approksimatsiya razlozheniya Teilora-Ito i konechno-raznostnye metody chislennogo integrirovaniya stokhasticheskikh differentsialnykh uravnenii Ito, Dep. v VINITI. 3509-B96, 1996 , 24 pp.  elib
126. O. Yu. Kulchitskii, D. F. Kuznetsov, Obobschenie razlozheniya Teilora na klass differentsiruemykh po Ito sluchainykh protsessov, Dep. v VINITI. 3508-B96, 1996 , 24 pp.  elib
127. O. Yu. Kulchitskii, D. F. Kuznetsov, “Chislennye Metody modelirovaniya reshenii stokhasticheskikh differentsialnykh uravnenii Ito”, The 1st International Scientific and Practical Conference “Differential Equations and Applications”, Abstracts (St.-Petersburg, 3–5 December, 1996), Izdatelstvo SPbGTU, S.-Peterburg, 1996, 135–136  elib
128. O. Yu. Kulchitsky, D. F. Kuznetsov, “The Taylor-Ito expansion of Ito processes, which are generated by solution of stochastic differential Ito equations”, The 1st International Scientific and Practical Conference “Differential Equations and Applications”, Abstracts (St.-Petersburg, 3–5 December, 1996), Izdatelstvo SPbGTU, S.-Peterburg, 1996, 137–138  elib
129. D. F. Kuznetsov, “The finte-difference methods for stochastic differential Ito equations”, The 1st International Scientific and Practical Conference “Differential Equations and Application”, Abstracts (St.-Petersburg, 3–5 December, 1996), Izdatelstvo SPbGTU, S.-Peterburg, 1996, 123–124  elib
130. O. Yu. Kulchitskii, D. F. Kuznetsov, Povtornye stokhasticheskie integraly i ikh svoistva, Dep. v VINITI. 3506-B96, 1996 , 29 pp.  elib
131. O. Yu. Kulchitskii, D. F. Kuznetsov, Obobschenie razlozheniya Teilora na klass sluchainykh protsessov, porozhdennykh resheniyami stokhasticheskikh differentsialnykh uravnenii Ito, Dep. v VINITI. 3507-B96, 1996 , 25 pp.  elib
132. O. Yu. Kulchitskii, D. F. Kuznetsov, “Chislennoe modelirovanie stokhasticheskikh sistem upravleniya, opisyvaemykh sistemami differentsialnykh uravnenii Ito”, Tretya ukrainskaya konferentsiya po avtomaticheskomu upravleniyu “Avtomatika 96” (Sevastopol, 9–14 sentyabrya, 1996), T.1, Izdatelstvo Sevastopolskogo tekhnicheskogo universiteta, Sevastopol, 1996, 162–163  elib
133. D. F. Kuznetsov, Metody chislennogo modelirovaniya reshenii sistem stokhasticheskikh differentsialnykh uravnenii Ito v zadachakh mekhaniki, diss. … kand. fiz.-matem. nauk, S.-Peterburg, 1996 , 248 pp.  elib
134. O. Yu. Kulchitskii, D. F. Kuznetsov, Metody chislennogo integrirovaniya nelineinykh stokhasticheskikh differentsialnykh uravnenii Ito, osnovannye na razlozhenii Teilora-Ito, Dep. v VINITI. 0127-V96, 1996 , 24 pp.  elib
135. O. Yu. Kulchitskii, D. F. Kuznetsov, Konechno-raznostnye metody chislennogo integrirovaniya nelineinykh stokhasticheskikh differentsialnykh uravnenii Ito, Dep. v VINITI. 0128-V96, 1996 , 25 pp.  elib
136. O. Yu. Kulchitskii, D. G. Arsenev, D. V. Butenina, V. M. Ivanov, N. V. Kapustina, M. L. Korenevskii, T. P. Krasulina, D. F. Kuznetsov, Metody usredneniya v teorii adaptivnogo stokhasticheskogo upravleniya, Informatsionnyi byulleten RFFI “Matematika, informatika, mekhanika”, # 4, 1996  elib

   1995
137. O. Yu. Kulchitskii, D. F. Kuznetsov, “O probleme korrektnogo modelirovaniya reshenii sistem stokhasticheskikh differentsialnykh uravnenii Ito”, Mekhanika i protsessy upravleniya. Sbornik nauchnykh trudov. “Trudy SPbGTU”, # 458, Izdatelstvo SPbGTU, S.-Peterburg, 1995, 162–168  elib

   1994
138. O. Yu. Kulchitskii, D. F. Kuznetsov, Approksimatsiya kratnykh stokhasticheskikh integralov Ito, Dep. v VINITI, 1678-B94, 1994 , 42 pp.  elib

   1993
139. O. Yu. Kulchitskii, D. F. Kuznetsov, Razlozhenie protsessov Ito v ryad Teilora - Ito v okrestnosti fiksirovannogo momenta vremeni, Dep. v VINITI, 2637-B93, 1993 , 26 pp.  elib

Presentations in Math-Net.Ru
1. Expansions of iterated Ito and Stratonovich stochastic integrals. The case of arbitrary CONS in L2[t, T]
D. F. Kuznetsov
9th International Conference on Stochastic Methods
June 7, 2024 11:30   
2. Application of Multiple Fourier-Legendre Series to the Implementation of Strong Exponential Milstein and Wagner-Platen Methods for Non-Commutative Semilinear SPDEs
Dmitriy Kuznetsov
5th International Conference on Stoсhastic Methods 2020
November 26, 2020 15:30   

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