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

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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.
Original languageEnglish
Pages (from-to)1213-1226
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number5
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • brownian motion
  • backward Euler–Maruyama
  • almost sure exponential stability
  • markov chain

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