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Aufsatz / Paper in SCI-Expanded-Zeitschrift

A Structural Analysis of Asymptotic Mean-square Stability for Multi-dimensional Linear Stochastic Differential Systems

Buckwar E., Sickenberger T.: A Structural Analysis of Asymptotic Mean-square Stability for Multi-dimensional Linear Stochastic Differential Systems, in: Applied Numerical Mathematics, Volume 62, Number 7, Page(s) 842–859, 2012.

BibTeX

@ARTICLE{
title = {A Structural Analysis of Asymptotic Mean-square Stability for Multi-dimensional Linear Stochastic Differential Systems},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Sickenberger, Thorsten},
language = {EN},
abstract = {We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the Theta-Maruyama and the Theta-Milstein method in this context. We propose an approach, based on the vectorisation of matrices and the Kronecker product, that allows us to deal efficiently with the matrix expressions arising in this analysis and that provides the explicit structure of the stability matrices in the general case of linear systems of SDEs. For a set of simple test SDE systems, incorporating different noise structures but only a few parameters, we apply the general results and provide visual and numerical comparisons of the stability properties of the two methods.},
pages = {842–859},
publisher = {Elsevier B.V. and IMAC},
journal = {Applied Numerical Mathematics},
volume = {62},
number = {7},
issn = {0168-9274},
month = {3},
year = {2012},
}

Details

Zusammenfassung: We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the Theta-Maruyama and the Theta-Milstein method in this context. We propose an approach, based on the vectorisation of matrices and the Kronecker product, that allows us to deal efficiently with the matrix expressions arising in this analysis and that provides the explicit structure of the stability matrices in the general case of linear systems of SDEs. For a set of simple test SDE systems, incorporating different noise structures but only a few parameters, we apply the general results and provide visual and numerical comparisons of the stability properties of the two methods.

Journal: Applied Numerical Mathematics
Volume: 62
Nummer: 7
Erscheinungsjahr: 2012
Seitenreferenz: 842–859
Anzahl Seiten: 18
Verlag: Elsevier B.V. and IMAC
ISSN: 0168-9274
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Thorsten Sickenberger

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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