# Almost Sure Decay Stability of the Backward Euler-Maruyama Scheme for Stochastic Differential Equations with Unbounded Delay

## Abstract:

This paper deals with analytical and numerical stability properties of highly nonlinear stochastic differential equations (SDEs) with unbounded delay. Sufficient conditions for almost sure decay stability of previous system, almost sure decay stability of the backward Euler-Maruyama (BEM) methods are investigated. In \cite{Wu2010} and \cite{Mao2011}, the authors consider one-side linear growth condition and sufficient small step size. In this paper, we consider the monotone condition, which is weaker than one-side linear growth condition. And we only need a very weak restriction of the step size. Different from \cite{Szpruch2010}, Szpruch and Mao consider the asymptotic stability of the numerical approximate. In this paper we consider the almost sure decay stability of the numerical solution. This improves the existing results greatly.

## Info:

Periodical:

Edited by:

Yuning Zhong

Pages:

39-44

Citation:

L. Chen and F. K. Wu, "Almost Sure Decay Stability of the Backward Euler-Maruyama Scheme for Stochastic Differential Equations with Unbounded Delay", Applied Mechanics and Materials, Vol. 235, pp. 39-44, 2012

Online since:

November 2012

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\$38.00

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