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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 7, Pages 1108–1120
DOI: https://doi.org/10.31857/S004446690001460-7 (Mi zvmmf10748) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations

D. F. Kuznetsov

St. Petersburg Polytechnical University, St. Petersburg, Russia
Citations (7)
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DOI: https://doi.org/10.31857/S004446690001460-7
Abstract: This paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equations, which are proper mathematical models of various dynamic systems affected by random disturbances, has not been adequately studied. This paper partially fills this gap.
Key words: multiple Fourier series, Legendre polynomials, repeated stochastic integral, Ito stochastic integral, Stratonovich stochastic integral, stochastic analog of Taylor's formula, Ito stochastic differential equation, numerical integration, mean square convergence.
Received: 12.09.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 7, Pages 1058–1070
DOI: https://doi.org/10.1134/S0965542518070096
Bibliographic databases:
Document Type: Article
UDC: 519.245
Language: Russian
Citation: D. F. Kuznetsov, “Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1108–1120; Comput. Math. Math. Phys., 58:7 (2018), 1058–1070
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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