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

 
PIIS004446690001460-7-1
DOI10.31857/S004446690001460-7
Publication type Article
Status Published
Authors
Affiliation: St. Petersburg Polytechnic University of Peter the Great
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 7
Pages1108-1120
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.

Keywordsmultiple 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
Received11.10.2018
Publication date11.10.2018
Number of characters600
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