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

TL;DR

This paper investigates limit theorems for small random perturbations in a planar impulsive dynamical system with state-dependent impulses, providing small noise expansions and error estimates.

Contribution

It introduces a small noise expansion for the radial component of a state-dependent impulsive system with rigorous error bounds.

Findings

Derived limit theorems for perturbed impulsive systems

Obtained small noise expansion with error estimates

Analyzed the radial component in polar coordinates

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.