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

^*Corresponding author for this work

Institute of Mathematics

5 Citations (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.

Original language	English
Journal	Applied Numerical Mathematics
Volume	158
Pages (from-to)	264-270
Number of pages	7
ISSN	0168-9274
DOIs	https://doi.org/10.1016/j.apnum.2020.08.002
Publication status	Published - 12.2020

Funding

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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T1 - High order numerical integrators for single integrand Stratonovich SDEs

AU - Cohen, David

AU - Debrabant, Kristian

AU - Rößler, Andreas

PY - 2020/12

Y1 - 2020/12

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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