Approximation properties for solutions to non-Lipschitz stochastic differential equations with Levy noise

被引：48

作者：

Xu, Yong ^{[1
]}

Pei, Bin ^{[1
]}

Li, Yongge ^{[1
]}

机构：

[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 11期

关键词：

approximation theorems; non-Lipschitz condition; Levy noise; stochastic differential equations; stochastic functional differential equations; SUCCESSIVE-APPROXIMATIONS; AVERAGING PRINCIPLE; DYNAMICAL-SYSTEMS; DRIVEN; STABILITY; JUMPS;

D O I：

10.1002/mma.3208

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the non-Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Levy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non-Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright (c) 2014 John Wiley & Sons, Ltd.

引用

页码：2120 / 2131

页数：12

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