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

Moderate deviations of density-dependent Markov chains