Fluctuation analysis for a randomly perturbed dynamical system with state-dependent impulse effects

Abstract

The principal aim of the present work is to explore limit theorems for small random perturbations of a planar impulsive dynamical system, where impulses occur at hitting times of a suitable switching surface, and are thus state-dependent. Working with a simplified example in polar coordinates, we obtain-for any fixed time horizon-a small noise expansion for the radial component, together with rigorous error estimates in the Skorohod space of right-continuous functions with left limits.