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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Stochastic Runge-Kutta methods for Itô SODEs with small noise

Buckwar E., Rößler A., Winkler R.: Stochastic Runge-Kutta methods for Itô SODEs with small noise, in: SIAM Journal on Scientific Computing, Volume 32, Number 4, Page(s) 1789-1808, 2010.

BibTeX

@ARTICLE{
title = {Stochastic Runge-Kutta methods for Itô SODEs with small noise},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Rößler, Andreas and Winkler, Renate},
language = {EN},
abstract = {We consider stochastic Runge–Kutta methods for Itô stochastic ordinary differential equations, and study their mean-square convergence properties for problems with small multiplicative noise or additive noise. First we present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations, and a Maruyama term is used to discretize the diffusion. Further, we suggest improving the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals, and we present a suitable class of fully derivative-free methods. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth the effort. Simulation results illustrate the theoretical findings.},
pages = {1789-1808},
publisher = {Society for Industrial and Applied Mathematics, Philadelphia},
journal = {SIAM Journal on Scientific Computing},
volume = {32},
number = {4},
issn = {1064-8275},
year = {2010},
}

Details

Zusammenfassung: We consider stochastic Runge–Kutta methods for Itô stochastic ordinary differential equations, and study their mean-square convergence properties for problems with small multiplicative noise or additive noise. First we present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations, and a Maruyama term is used to discretize the diffusion. Further, we suggest improving the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals, and we present a suitable class of fully derivative-free methods. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth the effort. Simulation results illustrate the theoretical findings.

Journal: SIAM Journal on Scientific Computing
Volume: 32
Nummer: 4
Erscheinungsjahr: 2010
Seitenreferenz: 1789-1808
Anzahl Seiten: 20
Verlag: Society for Industrial and Applied Mathematics, Philadelphia
ISSN: 1064-8275
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Andreas Rößler, 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

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