High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs

Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then present a systematic procedure based on the framework of modified differential equations for the construction of stochastic integrators that capture the invariant measure of a wide class of ergodic SDEs (Brownian and Langevin dynamics) with an accuracy independent of the weak order of the underlying method. Numerical experiments confirm our theoretical findings.


Read More: http://epubs.siam.org/doi/abs/10.1137/130935616
Original languageEnglish
Pages (from-to)1600-1622
Number of pages23
JournalSiam journal on numerical analysis
Volume52
Issue number4
Early online date10 Jul 2014
DOIs
Publication statusPublished - 1 Aug 2014

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