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

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

Expansion of Multiple Stratonovich Stochastic Integrals of Second Multiplicity, Based on Double Fourier-Legendre Series Summarized by Prinsheim Method


Dmitriy Feliksovich Kuznetsov

Peter the Great Saint-Petersburg Polytechnic University
Russia, 195251, Saint-Petersburg, Polytechnicheskaya st., 29
Department of Higher Mathematics
Professor, Doctor of Physico-Mathematical Sciences


The article is devoted to the expansion of multiple Stratonovich stochastic integrals of 2nd multiplicity into double series of standard Gaussian random variables. The proof of the expansion is based on application of double Fourier-Legendre series, summarized by Prinsheim method. The results of the article can be applied to numerical integration of Ito stochastic differential equations.



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