Open Access
Translator Disclaimer
December 2006 Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems
Dror Givon, Ioannis G. Kevrekidis, Raz Kupferman
Commun. Math. Sci. 4(4): 707-729 (December 2006).

Abstract

We study the convergence of the slow (or "essential") components of singularly perturbed stochastic differential systems to solutions of lower dimensional stochastic systems (the "effective", or "coarse" dynamics). We prove strong, mean-square convergence in systems where both fast and slow components are driven by noise, with full coupling between fast and slow components. We analyze a class of "projective integration" methods, which consist of a hybridization between a standard solver for the slow components, and short runs for the fast dynamics, which are used to estimate the effect that the fast components have on the slow ones. We obtain explicit bounds for the discrepancy between the results of the projective integration method and the slow components of the original system.

Citation

Download Citation

Dror Givon. Ioannis G. Kevrekidis. Raz Kupferman. "Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems." Commun. Math. Sci. 4 (4) 707 - 729, December 2006.

Information

Published: December 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1115.60036
MathSciNet: MR2264816

Subjects:
Primary: 60H10
Secondary: 60F15 , 65C30

Keywords: Dimension reduction , projective integration , scale separation , singular perturbations , Stochastic differential equations

Rights: Copyright © 2006 International Press of Boston

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.4 • No. 4 • December 2006
Back to Top