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Aufsatz / Paper in SCI-Expanded-Zeitschrift

The numerical stability of stochastic ordinary differential equations with additive noise

Buckwar E., Kloeden P., Riedler M.: The numerical stability of stochastic ordinary differential equations with additive noise, in: Stochastics and Dynamics, Volume 11, Number 2-3, Page(s) 265-281, 2011.

BibTeX

@ARTICLE{
title = {The numerical stability of stochastic ordinary differential equations with additive noise},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Kloeden, Peter E. and Riedler, Martin},
language = {EN},
abstract = {An asymptotic stability analysis of numerical methods used for simulating stochastic differential equations with additive noise is presented. The initial part of the paper is intended to provide a clear definition and discussion of stability concepts for additive noise equation derived from the principles of stability analysis based on the theory of random dynamical systems. The numerical stability analysis presented in the second part of the paper is based on the semi-linear test equation dX(t) = (AX(t) + f(X(t))) dt + σ dW(t), the drift of which satisfies a contractive one-sided Lipschitz condition, such that the test equation allows for a pathwise stable stationary solution. The θ-Maruyama method as well as linear implicit and two exponential Euler schemes are analysed for this class of test equations in terms of the existence of a pathwise stable stationary solution. The latter methods are specifically developed for semi-linear problems as they arise from spatial approximations of stochastic partial differential equations.},
pages = {265-281},
publisher = {World Scientific, Singapore},
journal = {Stochastics and Dynamics},
volume = {11},
number = {2-3},
issn = {0219-4937},
year = {2011},
url = {http://www.worldscientific.com/toc/sd/11/02n03},
}

Details

Zusammenfassung: An asymptotic stability analysis of numerical methods used for simulating stochastic differential equations with additive noise is presented. The initial part of the paper is intended to provide a clear definition and discussion of stability concepts for additive noise equation derived from the principles of stability analysis based on the theory of random dynamical systems. The numerical stability analysis presented in the second part of the paper is based on the semi-linear test equation dX(t) = (AX(t) + f(X(t))) dt + σ dW(t), the drift of which satisfies a contractive one-sided Lipschitz condition, such that the test equation allows for a pathwise stable stationary solution. The θ-Maruyama method as well as linear implicit and two exponential Euler schemes are analysed for this class of test equations in terms of the existence of a pathwise stable stationary solution. The latter methods are specifically developed for semi-linear problems as they arise from spatial approximations of stochastic partial differential equations.

Journal: Stochastics and Dynamics
Volume: 11
Nummer: 2-3
Erscheinungsjahr: 2011
Seitenreferenz: 265-281
Anzahl Seiten: 17
Web: http://www.worldscientific.com/toc/sd/11/02n03 (Journal Issue)
Verlag: World Scientific, Singapore
ISSN: 0219-4937
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Prof. Dr. Peter E. Kloeden, DI Ph.D. Martin Riedler

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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