Features of the Expansion of Multiple Stochastic Stratonovich Integrals Using Walsh and Haar Functions

Abstract

The problem of the root-mean-square convergence for approximations of multiple stochastic Stratonovich integrals based on the generalized multiple Fourier series method using Walsh and Haar functions is considered. It is shown that when they are chosen to expand multiple stochastic integrals, the proof of the root-mean-square convergence of a subsequence of series partial sums, which is formed in a way that is quite natural for these functions, does not require the explicit fulfillment of any additional conditions, except for the condition of the existence of the multiple stochastic Stratonovich integral.