Strong averaging principle for two-time-scale non-autonomous stochastic FitzHugh-Nagumo system with jumps

In this paper, we study an averaging principle for stochastic FitzHugh-Nagumo system with different time scales driven by cylindrical Wiener processes and Poisson jumps, where the slow equation is non-autonomous and the fast equation is autonomous case. Under suitable assumptions, we show that the s...

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Bibliographic Details
Published in:Journal of mathematical physics 2016-09, Vol.57 (9), p.1
Main Authors: Xu, Jie, Miao, Yu, Liu, Jicheng
Format: Article
Language:English
Subjects:
Convergence
Oscillators
Physics
Poisson distribution
Stochastic models
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Summary:In this paper, we study an averaging principle for stochastic FitzHugh-Nagumo system with different time scales driven by cylindrical Wiener processes and Poisson jumps, where the slow equation is non-autonomous and the fast equation is autonomous case. Under suitable assumptions, we show that the slow component mean-square strongly converges to the solution of the corresponding averaging equation, and the rate of the convergence as a by-product is also affirmed. Finally, we give some open problems which are derived from this paper.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4963173