THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED ONE-SIDED LIPSCHITZ CONDITION  

作　　者：Yidan Geng Minghui Song Mingzhu Liu 

机构地区：[1]School of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]Digital Technology Research Center,China Electronics Standardization Institute,Beijing100007,China

出　　处：《Journal of Computational Mathematics》2023年第4期663-682,共20页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.11671113,12071101).

摘　　要：In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.

关 键 词：Stochastic differential equations Piecewise continuous argument One-sided Lipschitz condition Truncated Euler-Maruyama method 

分 类 号：O175.2[理学—数学]