Year: 2009
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 659–679
Abstract
In this paper, the semi-implicit Euler (SIE) method for the stochastic differential delay equations with Poisson jump and Markov switching (SDDEwPJMSs) is developed. We show that under global Lipschitz assumptions the numerical method is convergent and SDDEwPJMSs is exponentially stable in mean-square if and only if for some sufficiently small step-size $\Delta$ the SIE method is exponentially stable in mean-square. We then replace the global Lipschitz conditions with local Lipschitz conditions and the assumptions that the exact and numerical solution have a bounded $p$th moment for some $p > 2$ and give the convergence result.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-790
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 659–679
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Poisson jump Lipschitz condition semi-implicit Euler method exponential stability convergence.