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Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

Part of: Stochastic analysis Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  19 September 2016

Xu Yang  and
Weidong Zhao
Xu Yang*
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China
Weidong Zhao*
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China
*
*Corresponding author. Email:dshyangxu@163.com (X. Yang), wdzhao@sdu.edu.cn (W. D. Zhao)
*Corresponding author. Email:dshyangxu@163.com (X. Yang), wdzhao@sdu.edu.cn (W. D. Zhao)
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Abstract

In this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

Keywords

Split-step schemestrong convergencestochastic differential equationjump-diffusionone-side Lipschitz condition

MSC classification

Secondary: 65C20: Models, numerical methods 60H35: Computational methods for stochastic equations 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 1004 - 1022
Copyright
Copyright © Global-Science Press 2016 

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