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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 7, Pages 1108–1120 (Mi zvmmf10748)  

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

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.

DOI: https://doi.org/10.31857/S004446690001460-7

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1058–1070

Bibliographic databases:

UDC: 519.245
Received: 12.09.2017

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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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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