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Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions

Other
Authors Annika Lang
Andreas Petersson
Andreas Thalhammer
Published in ArXiv
Publication year 2017
Published at Department of Mathematical Sciences
Language en
Links https://arxiv.org/abs/1702.07700
Subject categories Probability Theory and Statistics, Computational Mathematics

Abstract

The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. The purpose of this article is to discuss this property for approximations of infinite-dimensional stochastic differential equations and give necessary and sufficient conditions that ensure mean-square stability of the considered finite-dimensional approximations. Stability properties of typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler methods are characterized. Furthermore, results on their relationship to stability properties of the analytical solutions are provided. Simulations of the stochastic heat equation confirm the theory.

Page Manager: Webmaster|Last update: 9/11/2012
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