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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

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1569-397X
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Volume 19, Issue 2

Issues

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

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.

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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Xiaofeng Zong and Fuke Wu
Applied Mathematical Modelling, 2016, Volume 40, Number 1, Page 19
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Xuerong Mao
SIAM Journal on Numerical Analysis, 2015, Volume 53, Number 1, Page 370
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Wei Mao and Xuerong Mao
Abstract and Applied Analysis, 2013, Volume 2013, Page 1
[7]
Fuke Wu, Xuerong Mao, and Peter Kloeden
Discrete and Continuous Dynamical Systems, 2012, Volume 33, Number 2, Page 885

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