Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments  

作　　者：Ying Xie Chengjian Zhang 

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]School of Mathematics and Economics,Hubei University of Education,Wuhan 430205,China [3]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Science China Mathematics》2020年第12期2573-2594,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11971010);Scientific Research Project of Education Department of Hubei Province(Grant No.B2019184)。

摘　　要：This paper deals with numerical solutions of nonlinear stiff stochastic differential equations with jump-diffusion and piecewise continuous arguments.By combining compensated split-step methods and balanced methods,a class of compensated split-step balanced(CSSB)methods are suggested for solving the equations.Based on the one-sided Lipschitz condition and local Lipschitz condition,a strong convergence criterion of CSSB methods is derived.It is proved under some suitable conditions that the numerical solutions produced by CSSB methods can preserve the mean-square exponential stability of the corresponding analytical solutions.Several numerical examples are presented to illustrate the obtained theoretical results and the effectiveness of CSSB methods.Moreover,in order to show the computational advantage of CSSB methods,we also give a numerical comparison with the adapted split-step backward Euler methods with or without compensation and tamed explicit methods.

关 键 词：stiff stochastic differential equation jump diffusion piecewise continuous argument compensated split-step balanced method strong convergence mean-square exponential stability 

分 类 号：O211.63[理学—概率论与数理统计]