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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations

Buckwar E., Kelly C.: Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations, in: SIAM Journal on Numerical Analysis, Volume 48, Number 1, Page(s) 298-321, 2010.

BibTeX

@ARTICLE{
title = {Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Kelly, Cónall},
language = {EN},
abstract = {We develop two classes of test equations for the linear stability analysis of numerical methods applied to systems of stochastic ordinary differential equations of Itô type (SODEs). Motivated by the theory of stochastic stabilization and destabilization, these test equations capture certain fundamental effects of stochastic perturbation in systems of SODEs, while remaining amenable to analysis before and after discretization. We then carry out a linear stability analysis of the $\theta$-Maruyama method applied to these test equations, investigating mean-square and almost sure asymptotic stability of the test equilibria. We discuss the implications of our work for the notion of A-stability of the $\theta$-Maruyama method and use numerical simulation to suggest extensions of our results to test systems with nonnormal drift coefficients.},
pages = {298-321},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia},
journal = {SIAM Journal on Numerical Analysis},
volume = {48},
number = {1},
issn = {0036-1429},
year = {2010},
}

Details

Zusammenfassung: We develop two classes of test equations for the linear stability analysis of numerical methods applied to systems of stochastic ordinary differential equations of Itô type (SODEs). Motivated by the theory of stochastic stabilization and destabilization, these test equations capture certain fundamental effects of stochastic perturbation in systems of SODEs, while remaining amenable to analysis before and after discretization. We then carry out a linear stability analysis of the $\theta$-Maruyama method applied to these test equations, investigating mean-square and almost sure asymptotic stability of the test equilibria. We discuss the implications of our work for the notion of A-stability of the $\theta$-Maruyama method and use numerical simulation to suggest extensions of our results to test systems with nonnormal drift coefficients.

Journal: SIAM Journal on Numerical Analysis
Volume: 48
Nummer: 1
Erscheinungsjahr: 2010
Seitenreferenz: 298-321
Anzahl Seiten: 48
Verlag: Society for Industrial and Applied Mathematics (SIAM), Philadelphia
ISSN: 0036-1429
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Cónall Kelly

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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