Large deviations of Markov chains with multiple time-scales

Lea Popovic

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3319-3359

Abstract: For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a deterministic limit and a central limit theorem around it have already been proven in Kang and Kurtz (2013) and Kang et al. (2014). We present here a general approach to proving a large deviation principle in path space for such multi-scale Markov processes. Motivated by models arising in systems biology, we apply these large deviation results to general chemical reaction systems which exhibit multiple time-scales, and provide explicit calculations for several relevant examples.

Keywords: Large deviation principle; Multiple time-scales; Reaction networks; Markov chains; Jump diffusions; Piecewise deterministic Markov process; Comparison principle (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.09.009

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