An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure

被引：0
作者：
Wei Mao
Xuerong Mao
机构：
[1] Jiangsu Second Normal University,School of Mathematics and Information Technology
[2] University of Strathclyde,Department of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2016卷
关键词：
averaging principle; neutral SFDEs; convergence; convergence in probability; Poisson random measure;
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摘要：
In this paper, we study the averaging principle for neutral stochastic functional differential equations (SFDEs) with Poisson random measure. By stochastic inequality, Burkholder-Davis-Gundy’s inequality and Kunita’s inequality, we prove that the solution of the averaged neutral SFDEs with Poisson random measure converges to that of the standard one in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{p}$\end{document} sense and also in probability. Some illustrative examples are presented to demonstrate this theory.
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