Moderate deviations of density-dependent Markov chains

Xiaofeng Xue

Stochastic Processes and their Applications, 2021, vol. 140, issue C, 49-80

Abstract: A density dependent Markov chain (DDMC) introduced in Kurtz (1978) is a special continuous time Markov process. Examples are considered in fields like epidemics and processes which describe chemical reactions. Moreover the Yule process is a further example. In this paper we prove a moderate deviation principle for the paths of a certain class of DDMC. The proofs of the bounds utilize an exponential martingale as well as a generalized version of Girsanov’s theorem. The exponential martingale is defined according to the generator of the DDMC.

Keywords: Density-dependent Markov chain; Moderate deviation; Exponential martingale (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.06.005

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