# Moderate deviations of density-dependent Markov chains

## TL;DR

This paper establishes moderate deviation principles for density-dependent Markov chains, providing a probabilistic framework for understanding their path deviations under broad conditions.

## Contribution

It introduces moderate deviation principles for DDMC paths using exponential martingales and a generalized Girsanov's theorem, expanding theoretical understanding.

## Key findings

- Moderate deviation principles are proven for DDMC paths.
- The proofs utilize exponential martingales and a generalized Girsanov's theorem.
- Results apply under broad, generally satisfied assumptions.

## Abstract

The density-dependent Markov chain (DDMC) introduced in \cite{Kurtz1978} is a continuous time Markov process applied in fields such as epidemics, chemical reactions and so on. In this paper, we give moderate deviation principles of paths of DDMC under some generally satisfied assumptions. The proofs for the lower and upper bounds of our main result utilize an exponential martingale and a generalized version of Girsanov's theorem. The exponential martingale is defined according to the generator of DDMC.