High order numerical integrators for single integrand Stratonovich SDEs

David Cohen; Kristian Debrabant; Andreas Rößler

doi:10.1016/j.apnum.2020.08.002

High order numerical integrators for single integrand Stratonovich SDEs

David Cohen^*, Kristian Debrabant, Andreas Rößler

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

5 Zitate (Scopus)

Abstract

We show that applying any deterministic B-series method of order p_d with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order ⌊p_d/2⌋. As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.

Originalsprache	Englisch
Zeitschrift	Applied Numerical Mathematics
Jahrgang	158
Seiten (von - bis)	264-270
Seitenumfang	7
ISSN	0168-9274
DOIs	https://doi.org/10.1016/j.apnum.2020.08.002
Publikationsstatus	Veröffentlicht - 12.2020

Fördermittel

We appreciate the referees' comments on an earlier version of the paper. The work of DC was partially supported by the Swedish Research Council (VR) (projects nr. 2018-04443 ).

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10.1016/j.apnum.2020.08.002

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title = "High order numerical integrators for single integrand Stratonovich SDEs",

abstract = "We show that applying any deterministic B-series method of order pd with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order ⌊pd/2⌋. As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.",

author = "David Cohen and Kristian Debrabant and Andreas R{\"o}{\ss}ler",

year = "2020",

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doi = "10.1016/j.apnum.2020.08.002",

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AU - Cohen, David

AU - Debrabant, Kristian

AU - Rößler, Andreas

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N2 - We show that applying any deterministic B-series method of order pd with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order ⌊pd/2⌋. As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.

AB - We show that applying any deterministic B-series method of order pd with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order ⌊pd/2⌋. As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.

UR - https://www.scopus.com/pages/publications/85089486357

U2 - 10.1016/j.apnum.2020.08.002

DO - 10.1016/j.apnum.2020.08.002

M3 - Journal articles

AN - SCOPUS:85089486357

SN - 0168-9274

VL - 158

SP - 264

EP - 270

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

High order numerical integrators for single integrand Stratonovich SDEs

Abstract

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