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arXiv · 1905.03724

Application of the Method of Approximation of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations

Dmitriy F. Kuznetsov
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Abstract

We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated Ito stochastic integrals with respect to the scalar standard Wiener processes based on generalized multiple Fourier series. The case of multiple Fourier-Legendre series is considered in details. The results of the article can be applied to construction of high-order strong numerical methods (with respect to the temporal discretization) for the approximation of mild solution for non-commutative semilinear stochastic partial differential equations with multiplicative trace class noise.

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Dmitriy F. Kuznetsov. 2019-05-09. Application of the Method of Approximation of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations. https://arxiv.org/abs/1905.03724

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