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Soheili, Ali, Taherinasab, Yasser, Amini, Mohammad. (1399). Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems. سامانه مدیریت نشریات علمی, 1(1), 119-141. doi: 10.22054/jmmf.2020.54500.1011
Ali R. Soheili; Yasser Taherinasab; Mohammad Amini. "Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems". سامانه مدیریت نشریات علمی, 1, 1, 1399, 119-141. doi: 10.22054/jmmf.2020.54500.1011
Soheili, Ali, Taherinasab, Yasser, Amini, Mohammad. (1399). 'Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems', سامانه مدیریت نشریات علمی, 1(1), pp. 119-141. doi: 10.22054/jmmf.2020.54500.1011
Soheili, Ali, Taherinasab, Yasser, Amini, Mohammad. Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems. سامانه مدیریت نشریات علمی, 1399; 1(1): 119-141. doi: 10.22054/jmmf.2020.54500.1011

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

Journal of Mathematics and Modeling in Finance
دوره 1، شماره 1، خرداد 2021، صفحه 119-141    اصل مقاله (481.46 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22054/jmmf.2020.54500.1011
نویسندگان
Ali R. Soheili* 1؛ Yasser Taherinasab2؛ Mohammad Amini3
1Department of applied mathematics Ferdowsi university of Mashhad Mashhad, Iran
2Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Statistics, Ferdowsi University of Mashhad, Mashhad,
چکیده
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.
کلیدواژه‌ها
nonlinear stochastic differential equations؛ Poisson jump؛ compensated split-step ‎$theta‎$ method؛ one-sided Lipschitz condition؛ forward-backward Euler-Maruyama method؛ mean-square stability
مراجع
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[9] W. Mao, S. You and X. Mao, On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps, J. Comput. and Appl. Math., 301 (2016), pp. 1-15.
[10] E. Platen and N. Bruti-Liberati, Numerical Solution of Stochastic Differential Equations with Jumps in Finance, Springer-Verlag, Berlin, 2010.
[11] J. Tan, Z. Mu and Y. Guo, Convergence and stability of the compensated split-step θ method for stochastic differential equations with jumps, Advances in Difference Equations, 2014 (2014), pp. 1-19.
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