A local large deviation principle for inhomogeneous birth-death processes

TL;DR

This paper establishes a local large deviation principle for inhomogeneous birth-death processes with polynomially dependent jump rates, providing exponential asymptotics for the probability of specific process excursions.

Contribution

It introduces a local large deviation principle for inhomogeneous birth-death processes with polynomial asymptotics, extending existing large deviation theory.

Findings

Derived exponential asymptotics for process excursion probabilities

Established a local large deviation principle for inhomogeneous birth-death processes

Analyzed processes with polynomial rate dependence

Abstract

The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled process contained within a neighborhood of a given continuous non-negative function.