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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Almost sure asymptotic stability analysis of the Theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

Buckwar E., Kelly C., Rodkina A., Berkolaiko G.: Almost sure asymptotic stability analysis of the Theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations, in: LMS J. Comput. Math., Volume 15, Page(s) 71-83, 2012.

BibTeX

@ARTICLE{
title = {Almost sure asymptotic stability analysis of the Theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Kelly, Cónall and Rodkina, Alexandra and Berkolaiko, Gregory},
language = {EN},
abstract = {We perform an almost sure linear stability analysis of the Theta-Maruyama method, selecting as our test equation a two-dimensional system of Ito differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the Ito formula in the context of an almost sure linear stability analysis.},
pages = {71-83},
publisher = {Cambridge University Press},
journal = {LMS J. Comput. Math.},
volume = {15},
issn = {1461-1570},
year = {2012},
}

Details

Zusammenfassung: We perform an almost sure linear stability analysis of the Theta-Maruyama method, selecting as our test equation a two-dimensional system of Ito differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the Ito formula in the context of an almost sure linear stability analysis.

Journal: LMS J. Comput. Math.
Volume: 15
Erscheinungsjahr: 2012
Seitenreferenz: 71-83
Anzahl Seiten: 13
Verlag: Cambridge University Press
ISSN: 1461-1570
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Cónall Kelly, Prof. Dr. Alexandra Rodkina, Prof. Dr. Gregory Berkolaiko

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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