Abstract
The article is devoted to the expansions of multiple Stratonovich stochastic integrals of multiplicities 1-4 on the basis of the method of generalized multiple Fourier series. Mean-square convergence of the expansions for the case of Legendre polynomials and for the case of trigonometric functions is proven. The considered expansions contain only one operation of the limit transition in contrast to its existing analogues. This property is comfortable for the mean-square approximation of multiple stochastic integrals. The results of the article can be applied to numerical integration of Ito stochastic differential equations.
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