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

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.