A Lax equivalence theorem for stochastic differential equations

Authors:
Annika Lang
Affiliations:
Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131 Mannheim, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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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.