Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations

Yoshihito Kazashi

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arXiv · 1804.03355

Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations

Yoshihito Kazashi

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Abstract

An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A discrete analogue of maximal $L^2$-regularity of the scheme and the discretised stochastic convolution is established, which has the same form as their continuous counterpart.

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Yoshihito Kazashi. 2018-04-10. Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations. https://arxiv.org/abs/1804.03355

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