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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-order Strong Numerical Methods for Non-commutative Semilinear Stochastic Partial Differential Equations

Author(s):

Dmitriy Feliksovich Kuznetsov

Peter the Great Saint-Petersburg Polytechnic University
195251, Saint-Petersburg, Polytechnicheskaya ul., 29
Department of Higher Mathematics
Dr. Sc., Professor

sde_kuznetsov@inbox.ru

Abstract:

We consider a method for the approximation of iterated stochastic Ito integrals of arbitrary multiplicity with respect to the infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect to the finite-dimensional Wiener process based on generalized multiple Fourier series. The case of Fourier-Legendre series is considered in details. The results of the article can be applied to construction of high-order strong numerical methods (with respect to the temporal discretization) for a mild solution of non-commutative semilinear stochastic partial differential equations.

Keywords

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