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

Ashif Khan; Chetan D. Pahlajani

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arXiv · 2605.11877

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

Ashif Khan·Chetan D. Pahlajani

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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.

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Ashif Khan, Chetan D. Pahlajani. 2026-05-12. Fluctuation analysis for a randomly perturbed dynamical system with state-dependent impulse effects. https://arxiv.org/abs/2605.11877

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