Development and Application of the Fourier Method for the Numerical Solution of Ito Stochastic Differential Equations

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.

Keywords

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

11.10.2018

Publication date

11.10.2018

Number of characters

600

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GOST	Kuznetsov D. Development and Application of the Fourier Method for the Numerical Solution of Ito Stochastic Differential Equations // Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki – 2018. – V. 58. – Issue 7 C. 1108-1120 [Electronic resource]. URL: http://ras.jes.su/zvmmf/s207987840000702-1-1-en (circulation date: 17.09.2024). DOI: 10.31857/S004446690001460-7
MLA	Kuznetsov, D. "Development and Application of the Fourier Method for the Numerical Solution of Ito Stochastic Differential Equations." Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58.7 (2018):1108-1120. DOI: 10.31857/S004446690001460-7
APA	Kuznetsov D. (2018). Development and Application of the Fourier Method for the Numerical Solution of Ito Stochastic Differential Equations. Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58(7), pp.1108-1120 DOI: 10.31857/S004446690001460-7

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