Moderate deviations of density-dependent Markov chains

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 Girsanovs theorem. The exponential martingale is defined according to the generator of DDMC.