Pathwise accuracy and ergodicity of Metropolized integrators for SDEs

Nawaf Bou-Rabee, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

Metropolized integrators for ergodic stochastic differential equations (SDEs) are proposed that (1) are ergodic with respect to the (known) equilibrium distribution of the SDEs and (2) approximate pathwise the solutions of the SDEs on finitetime intervals. Both these properties are demonstrated in the paper, and precise strong error estimates are obtained. It is also shown that the Metropolized integrator retains these properties even in situations where the drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for SDEs typically become unstable and fail to be ergodic.

Original languageEnglish (US)
Pages (from-to)655-696
Number of pages42
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number5
DOIs
StatePublished - May 2010

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Ergodicity
Stochastic Equations
Differential equations
Differential equation
Equilibrium Distribution
Lipschitz
Error Estimates
Unstable
Interval

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Pathwise accuracy and ergodicity of Metropolized integrators for SDEs. / Bou-Rabee, Nawaf; Vanden Eijnden, Eric.

In: Communications on Pure and Applied Mathematics, Vol. 63, No. 5, 05.2010, p. 655-696.

Research output: Contribution to journalArticle

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