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Mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations

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Abstract

This paper deals with the mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations. It is shown that the stochastic theta methods inherit the mean-square exponential stability property of the underlying system. Moreover, the backward Euler method is mean-square exponentially stable with less restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.

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Authors and Affiliations

  1. School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan, 410075, China

    Qiyong Li & Siqing Gan

  2. Department of Mathematics, Huaihua University, Huaihua, Hunan, 418008, China

    Qiyong Li

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  1. Qiyong Li
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  2. Siqing Gan
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Correspondence to Qiyong Li.

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Li, Q., Gan, S. Mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations. J. Appl. Math. Comput. 39, 69–87 (2012). https://doi.org/10.1007/s12190-011-0510-3

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  • DOI: https://doi.org/10.1007/s12190-011-0510-3

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