Moderate deviations of hitting times of a family of density-dependent Markov chains

TL;DR

This paper establishes moderate deviation principles for hitting times of density-dependent Markov chains and their diffusion approximations, extending understanding of their probabilistic behavior in large but finite systems.

Contribution

It provides the first moderate deviation results for hitting times of density-dependent Markov chains and their diffusion limits, building on existing large deviation frameworks.

Findings

Moderate deviation principle for hitting times of density-dependent Markov chains.

Analogous moderate deviation results for diffusion approximations.

Connections between large deviations and hitting time behaviors.

Abstract

In this paper we are concerned with hitting times of a family of density-dependent Markov chains. A moderate deviation principle of the hitting time is given. The proof of the main theorem relies heavily on moderate deviations of density-dependent Markov chains given in \cite{Xue2021} and upper bounds of large deviations of Markov processes given in \cite{Dupuis1991}. An analogue moderate deviation of the hitting time of the diffusion approximation of the density-dependent Markov chain introduced in \cite{Ethier1986} is also given.