Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 33, Issue 2, Pages 885-903Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2013.33.885
Keywords
Moment exponential stability; Razumikhin-type theorem; Euler-Maruyama method; stochastic functional differential equations; stochastically perturbed equations
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Funding
- National Science Foundations of China [11001091, 61134012]
- Program for New Century Excellent Talents in University
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A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler-Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations.
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