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Kuznetsov, Dmitriy Feliksovich

Total publications: 125 (118)
in MathSciNet: 41 (40)
in zbMATH: 40 (40)
in Web of Science: 8 (8)
in Scopus: 31 (30)
Cited articles: 22
Citations in Math-Net.Ru: 23
Citations in Web of Science: 15
Citations in Scopus: 89
Presentations: 1

Number of views:
This page:25535
Abstract pages:1774
Full texts:426
References:107
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 stochastic Ito integral, iterated stochastic Stratonovich 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 (SPDE) 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 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$,$ mean of degree $p$ $(p>0)$ as well as with probability $1$) of iterated stochastic Ito 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}, $ $\psi_l(\tau):\ [t,\hspace{0.2mm} T]\to\mathbb {R},$ $l=1,\ldots,k$ are continuous deterministic functions$,$ ${\bf W}_{\tau} \in \mathbb{R^m}$ is a standard vector Wiener process with independent components ${\bf W}_{\tau}^{(i)},$ $i=1,\ldots,m\ $ and $\ {\bf W}_{\tau}^{(0)}:=\tau,\ $ $i_1,\ldots,i_k=0,\ 1,\ldots,m.$

Theorem on convergence with probability $1$ for expansions of iterated stochastic Ito integrals $(1)$ of arbitrary multiplicity $k\in\mathbb{N}$ has been fomulated and proved for continuously differentiable functions $\psi_{l}(\tau): [t, T] \to\mathbb {R},$ $l=1,\ldots,k$ as well as for multiple Fourier-Legendre series and multiple trigonometric Fourier series converging in the sense of norm in the space $L_2([t,\hspace{0.2mm} T]^k),$ $k\in \mathbb {N}.$

Generalizations of the Fourier method for complete orthonormal systems of functions with weight $r(t_1) \ldots r(t_k)$ 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 for iterated stochastic Stratonovich 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=\overline{1, 5},\ $ $\psi_l(\tau):\ [t,\hspace{0.2mm} T]\to\mathbb {R},\ $ $l=1,\ldots,k\ $ are smooth nonrandom functions$.$ These results can be interpreted as Wong-Zakai type theorems on the convergence of iterated Riemann-Stieltjes integrals of multiplicities 1-5 to iterated stochastic Stratonovich integrals. The hypothesis on expansion of iterated stochastic Stratonovich integrals of form $(2)$ for the case of arbitrary multiplicity $k\in \mathbb {N}$ has been formulated$.$

We formulated and proved two theorems on expansion of iterated stochastic Stratonovich integrals of form $(2)$ of arbitrary multiplicity $k\in \mathbb {N}$ based on generalized iterated Fourier series (converging pointwise) in complete orthonormal systems of functions in the space $L_2 ([t,\hspace{0.2mm} T]).$

Numerical simulation of iterated stochastic Ito and Stratonovich 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 stochastic Ito 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 $v\in H,~$ the functions $\psi_l(\tau),\ $ $l=1,\ldots, k,\ $ are the same as in $(1),~$ $Q:$ $U \rightarrow U$ 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 stochastic Ito and Stratonovich integrals $(1)$ and $(2)$ with multiplicities $1$ to $6.$ It is shown that the Legendre polynomial system is an optimal system for solving this problem.

Theorems on replacing the order of integration for iterated stochastic Ito 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 2005, 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., “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  crossref  mathscinet  zmath  isi  elib  scopus
  2. Kuznetsov D. F., “Expansion of iterated Stratonovich stochastic integrals, based on generalized multiple Fourier series”, "Ufa Mathematical Journal", 11:4 (2019), 49–77  mathnet  crossref  mathscinet  zmath  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  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  isi  elib  scopus
  5. Kuznetsov D. F., “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  crossref  mathscinet  zmath  isi  elib  scopus

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https://arxiv.org/a/kuznetsov_d_1

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |


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 FourierLegendre series to the implementation of strong exponential Milstein and WagnerPlaten methods for non-commutative semilinear SPDEs, The 5th International Conference On Stochastic Methods (ICSM-5), November 23-27, 2020, Moscow, Russia, Presentation PDF

   2021
3. 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, 2021 , 788 pp., (Monograph, In English), arXiv: 2003.14184  adsnasa  elib
4. 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, 27 arXiv.org articles, 2021 (Published online) , 1561 pp. PDF  elib
5. 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 PDF  crossref  mathscinet  zmath  elib  scopus (cited: 1)
6. 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 Springer  crossref  scopus (cited: 1)
7. 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  scopus
8. 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”, Electronic Journal “Differential Equations and Control Processes”, 2021, no. 4, A.1–A.787 (to appear)
9. Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Software Package, Gosudarstvennaya registratsiya programmy dlya EVM (RU2021616047), 2021 PDF  elib
10. Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Fourier-Legendre Coefficients Database, Gosudarstvennaya registratsiya bazy dannykh, okhranyaemoi avtorskimi pravami (RU2021620788), 2021 PDF  elib

   2020
11. 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  isi  elib  elib  scopus (cited: 3)
12. D. F. Kuznetsov, “Strong approximation of iterated Ito and Stratonovich stochastic integrals”, 4th International Conference on Stochastic Methods (ICSM-4) (Divnomorskoe, Russia, June 29, 2019), Theory of Probability and its Applications, 65, no. 1, 2020, 141–142 PDF  mathnet  mathnet  crossref  crossref  mathscinet  isi  elib  elib
13. 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) , 80 pp., arXiv: 2001.10192  adsnasa  elib
14. 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 PDF  crossref  mathscinet  zmath  elib  scopus (cited: 1)
15. 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 PDF  crossref  mathscinet  zmath  elib  scopus (cited: 3)
16. 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”, Electronic Journal “Differential Equations and Control Processes”, 2020, no. 4, A.1–A.606 PDF  crossref  mathscinet  zmath  elib  scopus (cited: 2)
17. 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
18. 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 , 29 pp., arXiv: 2006.16040  adsnasa
19. 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 , 336 pp., arXiv: 2009.14011  adsnasa  elib
20. 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 , 59 pp., arXiv: 2010.13564  adsnasa  elib
21. 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
22. 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 2327, 2020), RUDN Press, 2020, 88–92 PDF  elib

   2019
23. 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 (cited: 2)  elib  elib  scopus (cited: 8)
24. 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 (cited: 6)
25. 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) , 34 pp., arXiv: 1901.02345  adsnasa  elib
26. 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  isi (cited: 3)  elib  elib  scopus (cited: 9)
27. 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  adsnasa  elib
28. 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
29. 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) PDF  crossref  mathscinet  zmath  elib  scopus (cited: 8)
30. 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) , 20 pp., arXiv: 1807.00409  adsnasa  elib
31. 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 PDF  crossref  mathscinet  zmath  elib  scopus (cited: 2)
32. 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  adsnasa  elib

   2018
33. 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) , 57 pp., arXiv: 1801.01079  adsnasa  elib
34. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity based on generalized iterated Fourier series converging pointwise, 2018 (Published online) , 74 pp., arXiv: 1801.00784  adsnasa  elib
35. 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) , 59 pp., arXiv: 1801.01564  adsnasa  elib
36. 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) , 30 pp., arXiv: 1801.01962  adsnasa  elib
37. Dmitriy F. Kuznetsov, The hypotheses on expansions of iterated Stratonovich stochastic integrals of arbitrary multiplicity and their partial proof, 2018 (Published online) , 35 pp., arXiv: 1801.03195  adsnasa  elib
38. Dmitriy F. Kuznetsov, Integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales, 2018 (Published online) , 27 pp., arXiv: 1801.04634  adsnasa  elib
39. 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) , 41 pp., arXiv: 1801.05654  adsnasa  elib
40. 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) , 37 pp., arXiv: 1801.06501  adsnasa  elib
41. 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) , 18 pp., arXiv: 1801.07248  adsnasa  elib
42. 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) , 30 pp., arXiv: 1801.08862  adsnasa  elib
43. 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  isi (cited: 3)  elib  elib  scopus (cited: 9)
44. Dmitriy F. Kuznetsov, Expansion of iterated Stratonovich stochastic integrals of fifth multiplicity based on generalized multiple Fourier series, 2018 (Published online) , 38 pp., arXiv: 1802.00643  adsnasa  elib
45. 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) , 22 pp., arXiv: 1802.00888  adsnasa  elib
46. 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) , 31 pp., arXiv: 1802.04844  adsnasa  elib
47. 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) PDF  crossref  mathscinet  zmath  elib
48. 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 (cited: 7)  elib  elib  scopus (cited: 13)
49. 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) , 23 pp., arXiv: 1805.12527  adsnasa  elib
50. 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) , 24 pp., arXiv: 1806.10705  adsnasa  elib
51. 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) , 39 pp., arXiv: 1807.02190  adsnasa  elib
52. 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.1A.1073 (Published online) PDF, dopolnitelnaya ssylka: PDF  crossref  mathscinet  zmath  elib

   2017
53. 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
54. 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) , 46 pp., arXiv: 1712.08991  adsnasa  elib
55. Dmitriy F. Kuznetsov, Expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 based on generalized multiple Fourier series, 2017 (Published online) , 109 pp., arXiv: 1712.09516  adsnasa  elib
56. Dmitriy F. Kuznetsov, Expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series converging in the mean, 2017 (Published online) , 97 pp., arXiv: 1712.09746  adsnasa  elib
57. 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) , 100 pp., arXiv: 1801.00231  adsnasa  elib
58. 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) PDF  crossref  mathscinet  zmath  elib
59. 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) PDF  crossref  mathscinet  zmath  elib

   2013
60. 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
61. 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
62. 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
63. 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
64. 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
65. 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
66. 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) PDF  crossref  mathscinet  zmath  elib

   2009
67. 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
68. 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) PDF  crossref  zmath  elib

   2007
69. 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
70. 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
71. 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
72. D. F. Kuznetsov, Matematika. Teoriya funktsii kompleksnoi peremennoi, Uchebnoe posobie, Izdatelstvo Politekhnicheskogo universiteta, S.-Peterburg, 2006 , 124 pp.  elib

   2002
73. 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  elib  elib  scopus (cited: 1)  scopus (cited: 1)
74. 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  elib  elib  scopus (cited: 1)  scopus (cited: 1)
75. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, diss. … dokt. fiz.-matem. nauk, S.-Peterburg, 2002 , 490 pp.  elib
76. D. F. Kuznetsov, Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, Avtoreferat diss. dokt. fiz.-matem. nauk, Izdatelstvo SPbGTU, S.-Peterburg, 2002 , 34 pp.  elib

   2003
77. 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 (cited: 3)

   2001
78. 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 (cited: 2)
79. 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  elib  elib  scopus  scopus
80. 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
81. 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
82. 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 (cited: 2)  scopus (cited: 2)
83. 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
84. 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 (cited: 7)

   1999
85. 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
86. D. F. Kuznetsov, “K probleme chislennogo modelirovaniya stokhasticheskikh sistem”, Vestnik molodykh uchenykh. Seriya “Prikladnaya matematika i mekhanika”, 1999, no. 1, 20–32  elib
87. D. F. Kuznetsov, Chislennoe modelirovanie stokhasticheskikh differentsialnykh uravnenii i stokhasticheskikh integralov, Nauka, S.-Peterburg, 1999 , 460 pp., ISBN 5-02-024905-x  zmath  elib
88. D. F. Kuznetsov, Dva novykh predstavleniya razlozheniya Teilora-Stratonovicha, Preprint, Izdatelstvo SPbGTU, S.-Peterburg, 1999 , 13 pp. PDF  crossref  elib
89. D. F. Kuznetsov, Zamena poryadka integrirovaniya v povtornykh stokhasticheskikh integralakh po martingalu, Preprint, Izdatelstvo SPbGTU, S.-Peterburg, 1999 , 11 pp. PDF  crossref  elib
90. 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
91. 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) PDF  crossref  mathscinet  zmath  elib
92. 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
93. 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) PDF  crossref  mathscinet  zmath  elib
94. D. F. Kuznetsov, “Analiticheskie formuly dlya vychisleniya stokhasticheskikh integralov”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1998, no. 4, 18–28 PDF  crossref  mathscinet  zmath  elib
95. 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
96. 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  elib  elib  scopus  scopus

   1998
97. 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
98. 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
99. 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
100. 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
101. 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 (cited: 3)

   1997
102. 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) PDF  crossref  mathscinet  zmath  elib
103. D. F. Kuznetsov, Teoremy o zamene poryadka integrirovaniya v povtornykh stokhasticheskikh integralakh, Dep. v VINITI, 3607-B97, 1997 , 31 pp.  elib
104. O. Yu. Kulchitskii, D. F. Kuznetsov, “Unifitsirovannoe razlozhenie Teilora - Ito”, Elektronnyi zhurnal "Differentsialnye uravneniya i protsessy upravleniya, 1997, no. 1, 1–17 (Published online) PDF  crossref  mathscinet  zmath  elib
105. 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
106. 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
107. 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
108. 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
109. 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
110. 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
111. 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
112. 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
113. 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
114. 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
115. 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
116. O. Yu. Kulchitskii, D. F. Kuznetsov, Povtornye stokhasticheskie integraly i ikh svoistva, Dep. v VINITI. 3506-B96, 1996 , 29 pp.  elib
117. 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
118. 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
119. 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
120. 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
121. 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
122. 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
123. 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
124. O. Yu. Kulchitskii, D. F. Kuznetsov, Approksimatsiya kratnykh stokhasticheskikh integralov Ito, Dep. v VINITI, 1678-B94, 1994 , 42 pp.  elib

   1993
125. 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

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1. 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 Stohastic Methods 2020
November 26, 2020 15:30   

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