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Moderate deviations of density-dependent Markov chains

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  • Xue, Xiaofeng

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.

Suggested Citation

  • Xue, Xiaofeng, 2021. "Moderate deviations of density-dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 49-80.
    • Handle: RePEc:eee:spapps:v:140:y:2021:i:c:p:49-80
    DOI: 10.1016/j.spa.2021.06.005
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    References listed on IDEAS

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    1. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
    2. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    3. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
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    Cited by:

    1. He, Yuheng & Xue, Xiaofeng, 2023. "Moderate deviations of hitting times of a family of density-dependent Markov chains," Statistics & Probability Letters, Elsevier, vol. 195(C).

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