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arXiv · 1801.00784

Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise

Dmitriy F. Kuznetsov
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Abstract

The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on the generalized iterated Fourier series converging pointwise. The case of Fourier-Legendre series as well as the case of trigonometric Fourier series are considered in details. The obtained expansion provides a possibility to represent the iterated Stratonovich stochastic integral in the form of iterated series of products of standard Gaussian random variables. Convergence in the mean of degree $2n$ $(n\in \mathbb{N})$ of the expansion is proved. Some recent results on the expansion of iterated Stratonovich stochastic integrals of multiplicities 3 to 6 are given. The results of the article can be applied to the numerical solution of Ito stochastic differential equations.

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Dmitriy F. Kuznetsov. 2018-01-02. Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise. https://arxiv.org/abs/1801.00784

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