An expansion of multilpe Stratonovich stochastic integrals, based on multiple Fourier expansion

The expansion of multiple Stratonovich stochastic integrals of multiplicity $k$; $k\in N$ into multiple series of products of Gaussian random values is stated and proved. The coefficients of this expansion are the coefficients of multiple Fourier expansion of the function of several variables on full orthonormal systems in space $L_2([t,T])$. For expansion the convergence in mean of order $n$; $n\in N$ is proved. Some expansions of multiple Stratonovich stochastic integrals with the help of polynomial and trigonometric systems are considered.