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A Lax equivalence theorem for stochastic differential equations

Journal article
Authors Annika Lang
Published in Journal of Computational and Applied Mathematics
Volume 234
Issue 12
Pages 3387-3396
ISSN 0377-0427
Publication year 2010
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 3387-3396
Language en
Links dx.doi.org/10.1016/j.cam.2010.05.00...
Keywords Consistency , Convergence , Lax equivalence theorem , Numerical approximation , Stability , Stochastic partial differential equations
Subject categories Numerical analysis, Probability Theory and Statistics

Abstract

In this paper, a stochastic mean square version of Lax's equivalence theorem for Hilbert space valued stochastic differential equations with additive and multiplicative noise is proved. Definitions for consistency, stability, and convergence in mean square of an approximation of a stochastic differential equation are given and it is shown that these notions imply similar results as those known for approximations of deterministic partial differential equations. Examples show that the assumptions made are met by standard approximations. © 2010 Elsevier B.V. All rights reserved.

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