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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

CiteScore 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.177
Source Normalized Impact per Paper (SNIP) 2017: 0.592

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 19, Issue 2


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

Fuke Wu
  • School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China.
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/ Xuerong Mao / Peter E. Kloeden
Published Online: 2011-04-20 | DOI: https://doi.org/10.1515/ROSE.2011.010


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.

Keywords.: Stochastic functional differential equations (SFDEs); nonnegative semimartingale convergence theorem; almost sure stability; EM method

About the article

Received: 2010-10-07

Accepted: 2011-03-02

Published Online: 2011-04-20

Published in Print: 2011-06-01

Citation Information: Random Operators and Stochastic Equations, Volume 19, Issue 2, Pages 165–186, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/ROSE.2011.010.

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