High order numerical approximation of the invariant measure of Ergodic SDEs
High order numerical approximation of the invariant measure of Ergodic SDEs
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.
1600-1622
Abdulle, Assyr
ec277957-177a-4def-845a-d627d299238b
Vilmart, Gilles
60f6f7c2-9a15-41cd-9397-98bdd8800301
Zygalakis, Konstantinos C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6
2014
Abdulle, Assyr
ec277957-177a-4def-845a-d627d299238b
Vilmart, Gilles
60f6f7c2-9a15-41cd-9397-98bdd8800301
Zygalakis, Konstantinos C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6
Abdulle, Assyr, Vilmart, Gilles and Zygalakis, Konstantinos C.
(2014)
High order numerical approximation of the invariant measure of Ergodic SDEs.
SIAM Journal on Numerical Analysis, 52 (4), .
(doi:10.1137/130935616).
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.
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Published date: 2014
Organisations:
Applied Mathematics
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Local EPrints ID: 368130
URI: http://eprints.soton.ac.uk/id/eprint/368130
ISSN: 0036-1429
PURE UUID: 5279f0b4-8492-4a10-b53b-ae3beeb4d9c8
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Date deposited: 29 Aug 2014 13:28
Last modified: 14 Mar 2024 17:42
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Author:
Assyr Abdulle
Author:
Gilles Vilmart
Author:
Konstantinos C. Zygalakis
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