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2018 Discrete maximal regularity of an implicit Euler–Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations
Yoshihito Kazashi
Electron. Commun. Probab. 23: 1-14 (2018). DOI: 10.1214/18-ECP130

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. "Discrete maximal regularity of an implicit Euler–Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations." Electron. Commun. Probab. 23 1 - 14, 2018. https://doi.org/10.1214/18-ECP130

Information

Received: 20 October 2017; Accepted: 4 April 2018; Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 1390.60236
MathSciNet: MR3798240
Digital Object Identifier: 10.1214/18-ECP130

Subjects:
Primary: 60H15, 60H35

JOURNAL ARTICLE
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