On the averaging principle for stochastic delay differential equations with jumps

被引：0
|
作者：
Wei Mao
Surong You
Xiaoqian Wu
Xuerong Mao
机构：
[1] Jiangsu Second Normal University,School of Mathematics and Information Technology
[2] Donghua University,Department of Applied Mathematics
[3] University of Strathclyde,Department of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2015卷
关键词：
averaging principle; stochastic delay differential equations; Poisson random measure; convergence;
D O I：
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学科分类号：
摘要：
In this paper, we investigate the averaging principle for stochastic delay differential equations (SDDEs) and SDDEs with pure jumps. By the Itô formula, the Taylor formula, and the Burkholder-Davis-Gundy inequality, we show that the solution of the averaged SDDEs converges to that of the standard SDDEs in the sense of pth moment and also in probability. Finally, two examples are provided to illustrate the theory.
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