A Lax equivalence theorem for stochastic differential equations

被引：11

作者：

Lang, Annika ^{[1
]}

机构：

[1] Univ Mannheim, Fak Math & Informat, D-68131 Mannheim, Germany

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 12期

关键词：

Stochastic partial differential equations; Lax equivalence theorem; Numerical approximation; Consistency; Stability; Convergence;

D O I：

10.1016/j.cam.2010.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3387 / 3396

页数：10

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