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Title

Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems

Year: 1400
COI: JR_JMMF-1-1_008
Language: EnglishView: 52
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Authors

Ali Soheili - Department of applied mathematics Ferdowsi university of Mashhad Mashhad, Iran
Yasser Taherinasab - Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Mohammad Amini - Department of Statistics, Ferdowsi University of Mashhad, Mashhad,

Abstract:

In this paper, we analyze the strong convergence and stability of the Compensated Splite-step $theta$ (CSS$theta$) and Forward-Backward Euler-Maruyama (FBEM) methods for Numerical solutions of Stochastic Differential Equations with jumps (SDEwJs),where ‎$sqrt{2}-1leqthetaleq 1‎$. The drift term $f$ has a one-sided Lipschitz condition, the diffusion term $g$ and jump term $h$ satisfy global Lipschitz condition. Furthermore, we discuss about the stability of SDEwJs with constant coefficients and present new useful relations between their coefficients. Finally we examine the correctness and efficiency of theorems with some examples.In this paper, we analyze the strong convergence and stability of the Compensated Splite-step $theta$ (CSS$theta$) and Forward-Backward Euler-Maruyama (FBEM) methods for Numerical solutions of Stochastic Differential Equations with jumps (SDEwJs),where ‎$sqrt{2}-1leqthetaleq 1‎$. The drift term $f$ has a one-sided Lipschitz condition, the diffusion term $g$ and jump term $h$ satisfy global Lipschitz condition. Furthermore, we discuss about the stability of SDEwJs with constant coefficients and present new useful relations between their coefficients. Finally we examine the correctness and efficiency of theorems with some examples.

Keywords:

nonlinear stochastic differential equations, Poisson jump, compensated split-step ‎$theta‎$ method, one-sided Lipschitz condition, forward-backward Euler-Maruyama method, mean-square stability

Paper COI Code

This Paper COI Code is JR_JMMF-1-1_008. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1170171/

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Soheili, Ali and Taherinasab, Yasser and Amini, Mohammad,1400,Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems,https://civilica.com/doc/1170171

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