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Large deviations for Markov jump processes with uniformly diminishing rates

Author

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  • Agazzi, Andrea
  • Andreis, Luisa
  • Patterson, Robert I.A.
  • Renger, D.R. Michiel

Abstract

We prove a large-deviation principle (ldp) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the optimality of our assumptions on the decay of the jump rates. As a direct application of this work we relax the assumptions needed for the application of ldps to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise naturally particularly the context of mass action kinetics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:152:y:2022:i:c:p:533-559
    DOI: 10.1016/j.spa.2022.06.017
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    References listed on IDEAS

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    1. Popovic, Lea, 2019. "Large deviations of Markov chains with multiple time-scales," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3319-3359.
    2. Anderson, David F. & Cappelletti, Daniele & Kim, Jinsu & Nguyen, Tung D., 2020. "Tier structure of strongly endotactic reaction networks," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7218-7259.
    3. Hilder, Bastian & Peletier, Mark A. & Sharma, Upanshu & Tse, Oliver, 2020. "An inequality connecting entropy distance, Fisher Information and large deviations," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2596-2638.
    4. Adam Shwartz & Alan Weiss, 2005. "Large Deviations with Diminishing Rates," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 281-310, May.
    5. Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
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