On the averaging principle for stochastic delay differential equations with jumps

Advances in Difference Equations

Surong You¹  Xiaoqian Wu¹  Xuerong Mao²  Wei Mao³ 

[1] Department of Applied Mathematics, Donghua University, Shanghai, China;Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK;School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing, China

关键词: averaging principle;    stochastic delay differential equations;    Poisson random measure;    \(L^{p}\) convergence;   

DOI  :  10.1186/s13662-015-0411-0

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY