Moderate deviations for stochastic Cahn-Hilliard equations with a random dynamical boundary driven by Poisson random measures

Abstract

This work concerns a stochastic Cahn-Hilliard equation with a random dynamical boundary condition driven by Poisson random measures. Due to the disturbance of pure jump Lévy noise both in the domain and on its boundary, we drive the tightness of deviation processes by employing the stochastic control argument and the splitting method. With the help of the weak convergence approach, we establish the moderate deviations of this system, which bridge the gap between the central limit approximation and large deviations.