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Application of Multiple Fourier-Legendre Series to Implementation of Strong Exponential Milstein and Wagner-Platen 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:

The article is devoted to the application of multiple Fourier-Legendre series for the approximation of iterated stochastic Ito integrals of multiplicities 1 to 3 with respect to the infinite-dimensional Q-Wiener process. These iterated stochastic integrals are a part of the so-called exponential Milstein and Wagner-Platen numerical methods for semilinear stochastic partial differential equations with nonlinear multiplicative trace class noise. The mentioned numerical methods have strong orders of convergence 1.0- and 1.5- correspondingly with respect to the temporal discretization. The theorem on the mean-square convergence of approximations of iterated stochastic Ito integrals of multiplicities 1 to 3 with respect to the infinite-dimensional Q-Wiener process is formulated and proved. The results of this article can be applied to implementation of high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations with nonlinear multiplicative trace class noise.

Ключевые слова

Ссылки:

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