Stability and error analysis of an implicit Milstein finite difference scheme for a two-dimensional Zakai SPDE

被引：0
作者：
Christoph Reisinger
Zhenru Wang
机构：
[1] University of Oxford,Mathematical Institute
来源：
BIT Numerical Mathematics | 2019年 / 59卷
关键词：
Stochastic partial differential equations; Milstein scheme; Stochastic finite differences; Splitting schemes; Mean-square stability; -convergence; 65T50; 60H15; 65N06; 65N12;
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学科分类号：
摘要：
This article proposes an implicit finite difference scheme for a two-dimensional parabolic stochastic partial differential equation of Zakai type. The scheme is based on a Milstein approximation to the stochastic integral and an alternating direction implicit discretisation of the elliptic term. Mean-square stability and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-convergence of first order in time and second order in space are proven by Fourier analysis, in the presence of Dirac initial data. Numerical tests confirm these findings empirically.
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页码：987 / 1029
页数：42
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