On the averaging principle for stochastic delay differential equations with jumps

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Mao, Wei and You, Surong and Wu, Xiaoqian and Mao, Xuerong (2015) On the averaging principle for stochastic delay differential equations with jumps. Advances in Difference Equations, 2015. 70. ISSN 1687-1847 (https://doi.org/10.1186/s13662-015-0411-0)

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Abstract

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.

ORCID iDs

Mao, Wei, You, Surong, Wu, Xiaoqian and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
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