文章基本信息

标题：On the averaging principle for stochastic delay differential equations with jumps
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作者：Wei Mao ; Surong You ; Xiaoqian Wu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：70
DOI：10.1186/s13662-015-0411-0
语种：English
出版社：Hindawi Publishing Corporation
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.
关键词：averaging principle ; stochastic delay differential equations ; Poisson random measure ; (L^{p}) convergence