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

Mao, Wei and Mao, Xuerong (2016) An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure. Advances in Difference Equations, 2016 (1). 77. ISSN 1687-1847 (https://doi.org/10.1186/s13662-016-0802-x)

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Abstract

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 (Formula presented.) sense and also in probability. Some illustrative examples are presented to demonstrate this theory.

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