Poisson-noise induced escape from a metastable state

TL;DR

This paper derives comprehensive formulas for the probability distribution and escape rate of an overdamped particle in a potential well driven by Poisson noise, covering all pulse rate regimes from slow to fast.

Contribution

It provides a complete analytical solution for the distribution and escape rate in Poisson-noise driven systems, including exponents and prefactors, applicable across all pulse rates.

Findings

Formulas valid for all pulse rates from slow to fast.

Explicit expressions for exponents and prefactors.

Applicable to overdamped particles in potential wells.

Abstract

We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a potential well. The results apply for an arbitrary average rate of noise pulses, from slow pulse rates, where the noise acts on the system as strongly non-Gaussian, to high pulse rates, where the noise acts as effectively Gaussian.