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

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 Xue (2021) and upper bounds of large deviations of Markov processes given in Dupuis et al. (1991). An analogue moderate deviation of the hitting time of the diffusion approximation of the density-dependent Markov chain introduced in Ethier and Kurtz (1986) is also given.