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

Electronic Communications in Probability

Yoshihito Kazashi¹ 

关键词: multiplicative noise;    non-uniform time discretisation;    implicit Euler–Maruyama scheme;   

DOI  :  10.1214/18-ECP130

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY