# FUN-Veranstaltungen

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# Kontakt

Abteilung Forschungsunterstützung (FUN):
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# Forschungseinheiten

Aufsatz / Paper in SCI-Expanded-Zeitschrift

## Multistep methods for SDEs and their application to problems with small noise

Buckwar E., Winkler R.: Multistep methods for SDEs and their application to problems with small noise, in: SIAM Journal on Numerical Analysis, Volume 44, Number 2, Page(s) 779-803, 2006.

BibTeX

@ARTICLE{
title = {Multistep methods for SDEs and their application to problems with small noise},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Winkler, Renate},
language = {EN},
abstract = {In this article the numerical approximation of solutions of Itô stochastic differential equations is considered, in particular for equations with a small parameter $\epsilon$ in the noise coefficient. We construct stochastic linear multistep methods and develop the fundamental numerical analysis concerning their mean-square consistency, numerical stability in the mean-square sense and mean-square convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency. Further, for the small noise case we obtain expansions of the local error in terms of the step size and the small parameter $\epsilon$. Simulation results using several explicit and implicit stochastic linear $k$-step schemes, $k=1,\;2$, illustrate the theoretical findings.},
pages = {779-803},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia},
journal = {SIAM Journal on Numerical Analysis},
volume = {44},
number = {2},
issn = {0036-1429},
year = {2006},
}

### Details

Zusammenfassung: In this article the numerical approximation of solutions of Itô stochastic differential equations is considered, in particular for equations with a small parameter $\epsilon$ in the noise coefficient. We construct stochastic linear multistep methods and develop the fundamental numerical analysis concerning their mean-square consistency, numerical stability in the mean-square sense and mean-square convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency. Further, for the small noise case we obtain expansions of the local error in terms of the step size and the small parameter $\epsilon$. Simulation results using several explicit and implicit stochastic linear $k$-step schemes, $k=1,\;2$, illustrate the theoretical findings.

Journal: SIAM Journal on Numerical Analysis
Volume: 44
Nummer: 2
Erscheinungsjahr: 2006
Seitenreferenz: 779-803
Anzahl Seiten: 15
Verlag: Society for Industrial and Applied Mathematics (SIAM), Philadelphia
ISSN: 0036-1429
Reichweite: International

### Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Dr. Renate Winkler

Forschungseinheiten der JKU:

Wissenschaftszweige: 1103 Analysis | 1113 Mathematische Statistik | 1114 Numerische Mathematik | 1118 Wahrscheinlichkeitstheorie | 1121 Operations Research | 1145 Zeitreihenanalyse | 1165 Stochastik | 5943 Risikoforschung