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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

Buckwar E., Baker C.: Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations, in: Journal of Computational and Applied Mathematics, Volume 184, Number 2, Page(s) 404-427, 2005.

BibTeX

@ARTICLE{
title = {Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Baker, Christopher T.H. },
language = {EN},
abstract = {One concept of the stability of a solution of an evolutionary equation relates to the sensitivity of the solution to perturbations in the initial data; there are other stability concepts, notably those concerned with persistent perturbations. Results are presented on the stability in p-th mean of solutions of stochastic delay differential equations with multiplicative noise, and of stochastic delay difference equations. The difference equations are of a type found in numerical analysis and we employ our results to obtain mean-square stability criteria for the solution of the Euler–Maruyama discretization of stochastic delay differential equations. The analysis proceeds as follows: We show that an inequality of Halanay type (derivable via comparison theory) can be employed to derive conditions for p-th mean stability of a solution. We then produce a discrete analogue of the Halanay-type theory, that permits us to develop a p-th mean stability analysis of analogous stochastic difference equations. The application of the theoretical results is illustrated by deriving mean-square stability conditions for solutions and numerical solutions of a constant-coefficient linear test equation.},
pages = {404-427},
publisher = {Elsevier Science B.V. (North-Holland), Amsterdam},
journal = {Journal of Computational and Applied Mathematics},
volume = {184},
number = {2},
issn = {0377-0427},
year = {2005},
}

Details

Zusammenfassung: One concept of the stability of a solution of an evolutionary equation relates to the sensitivity of the solution to perturbations in the initial data; there are other stability concepts, notably those concerned with persistent perturbations. Results are presented on the stability in p-th mean of solutions of stochastic delay differential equations with multiplicative noise, and of stochastic delay difference equations. The difference equations are of a type found in numerical analysis and we employ our results to obtain mean-square stability criteria for the solution of the Euler–Maruyama discretization of stochastic delay differential equations. The analysis proceeds as follows: We show that an inequality of Halanay type (derivable via comparison theory) can be employed to derive conditions for p-th mean stability of a solution. We then produce a discrete analogue of the Halanay-type theory, that permits us to develop a p-th mean stability analysis of analogous stochastic difference equations. The application of the theoretical results is illustrated by deriving mean-square stability conditions for solutions and numerical solutions of a constant-coefficient linear test equation.

Journal: Journal of Computational and Applied Mathematics
Volume: 184
Nummer: 2
Erscheinungsjahr: 2005
Seitenreferenz: 404-427
Anzahl Seiten: 24
Verlag: Elsevier Science B.V. (North-Holland), Amsterdam
ISSN: 0377-0427
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Prof. Dr. Christopher T.H. Baker

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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