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Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations

Mao, Xuerong and Shen, Yi and Gray, Alison (2011) Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations. Journal of Computational and Applied Mathematics, 235 (5). pp. 1213-1226. ISSN 0377-0427

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Abstract

This is a continuation of the first author's earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [1] is the global Lipschitz condition. However, we will show in this paper that without this global Lipschitz condition the EM method may not preserve the almost sure exponential stability. We will then show that the backward EM method can capture the almost sure exponential stability for a certain class of highly nonlinear hybrid SDEs.

Item type: Article
ID code: 29078
Keywords: brownian motion, backward Euler–Maruyama, almost sure exponential stability, markov chain, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 07 Mar 2011 23:24
Last modified: 17 Jun 2015 19:27
URI: http://strathprints.strath.ac.uk/id/eprint/29078

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