Application of Multiple Fourier-Legendre Series to Implementation of Strong Exponential Milstein and Wagner-Platen Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations

Abstract

The article is devoted to the application of multiple Fourier-Legendre series to implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations with multiplicative trace class noise. These methods have strong orders of convergence $1.0-\epsilon$ and $1.5-\epsilon$ correspondingly (here $\epsilon$ is an arbitrary small positive real number) with respect to the temporal discretization. The theorem on mean-square convergence of approximations of iterated stochastic integrals of multiplicities 1 to 3 with respect to the infinite-dimensional $Q$-Wiener process is formulated and proved. The results of the article can be applied to implementation of exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations with multiplicative trace class noise.

32 pages. Some changes along the text in the whole. arXiv admin note: substantial text overlap with arXiv:1905.03724

References in corpus (3)

• 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
• Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB
• Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations

Cited by in corpus (3)

• 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
• Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB
• Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations