Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments  

作　　者：Yidan Geng Minghui Song Yulan Lu Mingzhu Liu 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2021年第1期194-218,共25页高等学校计算数学学报（英文版）

基　　金：This work is supported by the National Natural Science Foundation of China(No.11671113);the National Postdoctoral Program for Innovative Talents(No.BX20180347).

摘　　要：In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.

关 键 词：Stochastic differential equations with piecewise continuous argument local Lips-chitz condition Khasminskii-type condition truncated Euler-Maruyama method convergence and stability 

分 类 号：O17[理学—数学]