 The stability with a general decay of stochastic delay differential equations with Markovian switchingTian Zhang and Huabin Chen Applied Mathematics and Computation, 2019, vol. 359, issue C, 294-307 Abstract: This paper considers the problems on the existence and uniqueness, the pth(p ≥ 1)-moment and the almost sure stability with a general decay for the global solution of stochastic delay differential equations with Markovian switching, when the drift term and the diffusion term satisfy the locally Lipschitz condition and the monotonicity condition. By using the Lyapunov function approach, the Barbalat Lemma and the nonnegative semi-martingale convergence theorem, some sufficient conditions are proposed to guarantee the existence and uniqueness as well as the stability with a general decay for the global solution of such equations. It is mentioned that, in this paper, the time-varying delay is a bounded measurable function. The derived stability results are more general, which not only include the exponential stability but also the polynomial stability as well as the logarithmic one. At last, two examples are given to show the effectiveness of the theoretical results obtained. Keywords: Stochastic delay differential equations; Stability; General decay; The existence and uniqueness; Markovian switching (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:359:y:2019:i:c:p:294-307 DOI: 10.1016/j.amc.2019.04.057 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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