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A Lax equivalence theorem for stochastic differential equations

Annika Lang (Institutionen för matematiska vetenskaper, matematisk statistik)
Journal of Computational and Applied Mathematics (0377-0427). Vol. 234 (2010), 12, p. 3387-3396.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Consistency , Convergence , Lax equivalence theorem , Numerical approximation , Stability , Stochastic partial differential equations



Denna post skapades 2014-07-09. Senast ändrad 2014-10-27.
CPL Pubid: 200346

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Numerisk analys
Sannolikhetsteori och statistik

Chalmers infrastruktur