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

An expansion of multiple Stratonovich stochastic integrals of multiplicity , 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 . The convergence in mean of order , is established. Some expansions of multiple Stratonovich stochastic integrals with the help of polynomial and trigonometric systems are considered. Bibliography: 8 titles.