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
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.
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.
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1058–1070
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
\paper Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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