Communications in Mathematical Sciences

Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems

Dror Givon, Ioannis G. Kevrekidis, and Raz Kupferman

Full-text: Open access

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.

Article information

Source
Commun. Math. Sci., Volume 4, Number 4 (2006), 707-729.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.cms/1175797607

Mathematical Reviews number (MathSciNet)
MR2264816

Zentralblatt MATH identifier
1115.60036

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F15: Strong theorems 65C30: Stochastic differential and integral equations

Keywords
Dimension reduction stochastic differential equations scale separation singular perturbations projective integration

Citation

Givon, Dror; Kevrekidis, Ioannis G.; Kupferman, Raz. Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems. Commun. Math. Sci. 4 (2006), no. 4, 707--729. https://projecteuclid.org/euclid.cms/1175797607


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