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

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О журнале История Журнала Издатель Адреса Тематика Редакторский состав Рецензирование Для авторов Издательская этика Коллекция номеров English version

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

Автор(ы):

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

Аннотация:

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.

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