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Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations

Wu, Fuke and Mao, Xuerong and Kloeden, Peter E. (2011) Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations. Random Operator and Stochastic Equations, 19 (2). pp. 105-216. ISSN 0926-6364

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Abstract

By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–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.