 Exponential stability of the split-step θ-method for neutral stochastic delay differential equations with jumpsHaoyi Mo, Feiqi Deng and Chaolong Zhang Applied Mathematics and Computation, 2017, vol. 315, issue C, 85-95 Abstract: The exponential mean-square stability of the split-step θ-method for neutral stochastic delay differential equations (NSDDEs) with jumps is considered. New conditions for jumps are proposed to ensure the exponential mean-square stability of the trivial solution. If the drift coefficient satisfies the linear growth condition, it is shown that the split-step θ-method can reproduce the exponential mean-square stability of the trivial solution for the constrained stepsize. Then by applying the Chebyshev inequality and the Borel–Cantelli lemma, the almost sure exponential stability of both the trivial solution and the numerical solution can be obtained. Since split-step θ-method covers Euler–Maruyama (EM) method and split-step backward Euler (SSBE) method, the conclusions are valid for these two methods. Moreover, they can adapt to the NSDDEs and the SDDEs with jumps. Finally, a numerical example illustrates the effectiveness of the theoretical results. Keywords: Neutral stochastic delay differential equations with jumps; Stochastic split-step θ-method; Exponential mean-square stability; Almost sure exponential stability (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:315:y:2017:i:c:p:85-95 DOI: 10.1016/j.amc.2017.06.034 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.