# FUN-Veranstaltungen

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# Kontakt

Abteilung Forschungsunterstützung (FUN):
forschen@jku.at

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# Forschungseinheiten

Aufsatz / Paper in SCI-Expanded-Zeitschrift

## On Halanay-type analysis of exponential stability for the θ-Maruyama method for stochastic delay differential equations

Buckwar E., Baker C.: On Halanay-type analysis of exponential stability for the θ-Maruyama method for stochastic delay differential equations, in: Stochastics and Dynamics, Volume 5, Number 2, Page(s) 201-209, 2005.

BibTeX

@ARTICLE{
title = {On Halanay-type analysis of exponential stability for the θ-Maruyama method for stochastic delay differential equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Baker, Christopher T.H. },
language = {EN},
abstract = {Using an approach that has its origins in work of Halanay, we consider stability in mean square of numerical solutions obtained from the θ-Maruyama discretization of a test stochastic delay differential equation dX(t)={f(t)-aX(t)+bX(t-\tau)}dt + {g(t)+\eta X(t)+\mu X(t-\tau)}dW(t), interpreted in the Itô sense, where W(t) denotes a Wiener process. We focus on demonstrating that we may use techniques advanced in a recent report by Baker and Buckwar to obtain criteria for asymptotic and exponential stability, in mean square, for the solutions of the recurrence X_{n+1}-X_n = θ h {f_{n+1} -a X_{n+1} +b X_{n+1-N}} + (1- θ h) {f_{n} -a X_{n} +b X_{n-N}} + \qrt{h} {g_n + \eta X_n + \mu X_{n-N} \xi_n, \xi_n \in N(0,1).},
pages = {201-209},
publisher = {World Scientific, Singapore},
journal = {Stochastics and Dynamics},
volume = {5},
number = {2},
issn = {0219-4937},
year = {2005},
}

### Details

Zusammenfassung: Using an approach that has its origins in work of Halanay, we consider stability in mean square of numerical solutions obtained from the θ-Maruyama discretization of a test stochastic delay differential equation dX(t)={f(t)-aX(t)+bX(t-\tau)}dt + {g(t)+\eta X(t)+\mu X(t-\tau)}dW(t), interpreted in the Itô sense, where W(t) denotes a Wiener process. We focus on demonstrating that we may use techniques advanced in a recent report by Baker and Buckwar to obtain criteria for asymptotic and exponential stability, in mean square, for the solutions of the recurrence X_{n+1}-X_n = θ h {f_{n+1} -a X_{n+1} +b X_{n+1-N}} + (1- θ h) {f_{n} -a X_{n} +b X_{n-N}} + \qrt{h} {g_n + \eta X_n + \mu X_{n-N} \xi_n, \xi_n \in N(0,1).

Journal: Stochastics and Dynamics
Volume: 5
Nummer: 2
Erscheinungsjahr: 2005
Seitenreferenz: 201-209
Anzahl Seiten: 9
Verlag: World Scientific, Singapore
ISSN: 0219-4937
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