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

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

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} 

• http://mi.mathnet.ru/eng/znsl519
• http://mi.mathnet.ru/eng/znsl/v244/p186

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
5. D. F. Kuznetsov, “Expansion of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series”, Ufa Math. J., 11:4 (2019), 49–77