Numerical solutions of SDEs with Markovian switching and jumps under non-Lipschitz conditions

被引：8

作者：

Chen, Yingzi ^{[1
,2
]}

Xiao, Aiguo ^{[1
,2
]}

Wang, Wansheng ^{[3
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[3] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 360卷

基金：

中国国家自然科学基金;

关键词：

Strong convergence; Stochastic differential equation; Markovian switching; Jump-diffusion; Non-Lipschitz conditions; One-sided Lipschitz condition; STOCHASTIC DIFFERENTIAL-EQUATIONS; STRONG-CONVERGENCE; STABILITY; APPROXIMATIONS; DIFFUSIONS;

D O I：

10.1016/j.cam.2019.03.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the numerical solutions to stochastic differential equations with Markovian switching and jumps under non-Lipschitz conditions are considered. Firstly, we study the existence and uniqueness of solutions to this class of equations. Then we present the moment bounds of the exact and numerical solutions. It is also proved that the strong rate of convergence of the Euler scheme is equal to 1/2 with the drift coefficient satisfying one-sided Lipschitz condition while the diffusion and jump coefficients satisfy global Lipschitz conditions. Some numerical examples are given to confirm the theoretical results. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：41 / 54

页数：14

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