Expansion of the Stratonovich Multiple Stochastic Integrals Based on the Fourier Multiple series

Abstract

An expansion of multiple Stratonovich stochastic integrals of multiplicity \(\user1{k,k} \in N\), into multiple series of products of Gaussian random variables is obtained. The coefficients of this expansion are the coefficients of multiple Fourier-series expansion of a function of several variables relative to a complete orthonormal system in the space \(\user1{L}_2 ([\user1{t,T}])\). The convergence in mean of order \(\user1{n, n} \in \user1{N}\), is established. Some expansions of multiple Stratonovich stochastic integrals with the help of polynomial and trigonometric systems are considered. Bibliography: 8 titles.