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Zap. Nauchn. Sem. POMI, 1997, Volume 244, Pages 186–204 (Mi znsl519)  

This article is cited in 5 scientific papers (total in 5 papers)

The unified Taylor–Ito Expansion

O. Yu. Kulchitskii, D. F. Kuznetsov

Saint-Petersburg State Polytechnical University

Abstract: The problem of the Taylor–Ito expansion of Ito processes in vicinity of a fixed moment of the time is considered. The Taylor–Ito expansion, which is known in a literature is transformed to the unified Taylor–Ito expansion using the system of the special repeated stohastic Ito integrals with polynomial weight functions. The unified Taylor–Ito expansion include a smaller number of different types of repeated stohastic integrals, than the Taylor–Ito expansion, which is known in a literature. There are the recurrent relations between the coefficients of the unified Taylor–Ito expansion. Therefore the unified Taylor–Ito expansion is more convenient for synthesis of algorithms of numerical solution of stochastic differential Ito equations.

Full text: PDF file (248 kB)

English version:
Journal of Mathematical Sciences (New York), 2000, 99:2, 1130–1140

Bibliographic databases:

UDC: 519.2
Received: 15.12.1997

Citation: O. Yu. Kulchitskii, D. F. Kuznetsov, “The unified Taylor–Ito Expansion”, Probability and statistics. Part 2, Zap. Nauchn. Sem. POMI, 244, POMI, St. Petersburg, 1997, 186–204; J. Math. Sci. (New York), 99:2 (2000), 1130–1140

Citation in format AMSBIB
\Bibitem{KulKuz97}
\by O.~Yu.~Kulchitskii, D.~F.~Kuznetsov
\paper The unified Taylor--Ito Expansion
\inbook Probability and statistics. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 244
\pages 186--204
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl519}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1700389}
\zmath{https://zbmath.org/?q=an:0957.60071}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 99
\issue 2
\pages 1130--1140
\crossref{https://doi.org/10.1007/BF02673635}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. F. Kuznetsov, “New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations”, Comput. Math. Math. Phys., 41:6 (2001), 874–888  mathnet  mathscinet  zmath
    2. 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”, Autom. Remote Control, 79:7 (2018), 1240–1254  mathnet  crossref  isi  elib
    3. D. F. Kuznetsov, “Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations”, Comput. Math. Math. Phys., 58:7 (2018), 1058–1070  mathnet  crossref  crossref  isi  elib
    4. D. F. Kuznetsov, “On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence”, Autom. Remote Control, 80:5 (2019), 867–881  mathnet  crossref  crossref  isi  elib
    5. D. F. Kuznetsov, “Expansion of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series”, Ufa Math. J., 11:4 (2019), 49–77  mathnet  crossref  isi
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