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The article is devoted to a new proof of the expansion for iterated Itostochastic integrals with respect to the components of a multidimensionalWiener process. The above expansion is based on Hermite polynomials andgeneralized multiple Fourier series in arbitrary complete orthonormal systemsof functions in a Hilbert space. In 2006, the author obtained a similarexpansion, but with a lesser degree of generality. Namely, for the case ofcontinuous or piecewise continuous complete orthonornal systems of functions ina Hilbert space. In this article, the author generalizes the expansion ofiterated Ito stochastic integrals obtained by him in 2006 to the case of anarbitrary complete orthonormal systems of functions in a Hilbert space using anew approach based on the Ito formula. The obtained expansion of iterated Itostochastic integrals is useful for constructing of high-order strong numericalmethods for systems of Ito stochastic differential equations withmultidimensional non-commutative noise.

differencialʹnye uravneniâ i processy upravleniâ

A new proof of the expansion of iterated Ito stochastic integrals with  respect to the components of a multidimensional Wiener process based on  generalized multiple Fourier series and Hermite polynomials