Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations
Wu, Fuke and Mao, Xuerong and Kloeden, Peter E. (2013) Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations. Discrete and Continuous Dynamical Systems - Series A, 33 (2). pp. 885-903. ISSN 1078-0947 (https://doi.org/10.3934/dcds.2013.33.885)
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Abstract
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.
ORCID iDs
Wu, Fuke, Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864 and Kloeden, Peter E.;-
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Item type: Article ID code: 46665 Dates: DateEventFebruary 2013PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 12 Feb 2014 12:48 Last modified: 21 Sep 2024 00:35 URI: https://strathprints.strath.ac.uk/id/eprint/46665