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

被引：9

作者：

Xu, Jie ^{[1
,2
]}

Miao, Yu ^{[1
,2
]}

Liu, Jicheng ^{[3
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Henan Normal Univ, Henan Engn Lab Big Data Stat Anal & Optimal Contr, Xinxiang 453007, Henan, Peoples R China

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 09期

关键词：

REACTION-DIFFUSION EQUATIONS; PARTIAL-DIFFERENTIAL-EQUATIONS; STRONG-CONVERGENCE RATE; NOISE;

D O I：

10.1063/1.4963173

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. Published by AIP Publishing.

引用

页数：21

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