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Large deviations of Markov chains with multiple time-scales

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  • Popovic, Lea

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.

Suggested Citation

  • Popovic, Lea, 2019. "Large deviations of Markov chains with multiple time-scales," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3319-3359.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3319-3359
    DOI: 10.1016/j.spa.2018.09.009
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    References listed on IDEAS

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    1. Jin Feng & Jean-Pierre Fouque & Rohini Kumar, 2010. "Small-time asymptotics for fast mean-reverting stochastic volatility models," Papers 1009.2782, arXiv.org, revised Aug 2012.
    2. Feng, Jin, 1999. "Martingale problems for large deviations of Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 165-216, June.
    3. Kumar, Rohini & Popovic, Lea, 2017. "Large deviations for multi-scale jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1297-1320.
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    Cited by:

    1. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    2. Agazzi, Andrea & Andreis, Luisa & Patterson, Robert I.A. & Renger, D.R. Michiel, 2022. "Large deviations for Markov jump processes with uniformly diminishing rates," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 533-559.

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