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 Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 8, Pages 1299–1313 (Mi zvmmf10933)

A comparative analysis of efficiency of using the legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations

D. F. Kuznetsov

Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251 Russia

Abstract: This paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the multiple stochastic integrals of multiplicity 1–3 appearing in the Ito–Taylor expansion as an example, it is shown that their expansions obtained using multiple Fourier–Legendre series are significantly simpler and less computationally costly than their analogs obtained on the basis of multiple trigonometric Fourier series. The results obtained in this paper can be useful for constructing and implementing strong numerical methods for solving Ito stochastic differential equations with multidimensional nonlinear noise.

Key words: multiple Fourier series, Legendre polynomials, multiple stochastic integral, Ito stochastic integral, Stratonovich stochastic integral, Ito–Taylor expansion, Ito stochastic differential equation, numerical integration, mean square convergence.

DOI: https://doi.org/10.1134/S0044466919080118

English version:
Computational Mathematics and Mathematical Physics, 2019, 59:8, 1236–1250

Bibliographic databases:

UDC: 519.245
Revised: 15.01.2019
Accepted:10.04.2019

Citation: D. F. Kuznetsov, “A comparative analysis of efficiency of using the legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:8 (2019), 1299–1313; Comput. Math. Math. Phys., 59:8 (2019), 1236–1250

Citation in format AMSBIB
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