A Lax equivalence theorem for stochastic differential equations
Artikel i vetenskaplig tidskrift, 2010

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.

Stability

Lax equivalence theorem

Stochastic partial differential equations

Numerical approximation

Consistency

Convergence

Författare

Annika Lang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Journal of Computational and Applied Mathematics

0377-0427 (ISSN)

Vol. 234 12 3387-3396

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

DOI

10.1016/j.cam.2010.05.001