Almost sure exponential stability of the Eulera-Maruyama approximations for stochastic functional differential equations

Fuke Wu, Xuerong Mao, Peter E Kloeden

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19 Citations (Scopus)


By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Eulera??Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately.
Original languageEnglish
Pages (from-to)165 - 186
Number of pages22
JournalRandom Operators and Stochastic Equations
Issue number2
Publication statusPublished - 2011
Externally publishedYes

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