Convergence and stability of modified partially truncated Euler-Maruyama method for stochastic differential equations with piecewise continuous arguments

被引：0

作者：

Shi, Hongling ^{[1
]}

Song, Minghui ^{[1
]}

Liu, Mingzhu ^{[1
]}

机构：

[1] Harbin Inst Technol, Sch Math, Harbin, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2023年 / 100卷 / 12期

关键词：

Modified partially truncated EM method; stochastic differential equations with piecewise continuous arguments; strong convergence; convergence rate; mean square exponential stability; TIME; STABILIZATION;

D O I：

10.1080/00207160.2023.2274278

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper constructs a modified partially truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift and diffusion coefficients grow superlinearly. We divide the coefficients of SDEPCAs into global Lipschitz continuous and superlinearly growing parts. Our method only truncates the superlinear terms of the coefficients to overcome the potential explosions caused by the nonlinearities of the coefficients. The strong convergence theory of this method is established and the 1/2 convergence rate is presented. Furthermore, an explicit scheme is developed to preserve the mean square exponential stability of the underlying SDEPCAs. Several numerical experiments are offered to illustrate the theoretical results.

引用

页码：2269 / 2289

页数：21

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