IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v152y2022icp533-559.html
   My bibliography  Save this article

Large deviations for Markov jump processes with uniformly diminishing rates

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001521
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.06.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Adam Shwartz & Alan Weiss, 2005. "Large Deviations with Diminishing Rates," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 281-310, May.
    4. Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
    5. Popovic, Lea, 2019. "Large deviations of Markov chains with multiple time-scales," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3319-3359.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Ad Ridder & Adam Shwartz, 2005. "Large deviations without principle: join the shortest queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 467-483, December.
    3. Ad Ridder & Adam Shwartz, 2005. "Large Deviations Methods and the Join-the-Shortest-Queue Model," Tinbergen Institute Discussion Papers 05-016/4, Tinbergen Institute.
    4. Kim-Hung Li & Cheuk Ting Li, 2019. "Linear Combination of Independent Exponential Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 253-277, March.
    5. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
    6. Kraaij, Richard C. & Mahé, Louis, 2020. "Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5453-5491.
    7. Ad Ridder & Adam Shwartz, 2004. "Large Deviations without Principle: Join the Shortest Queue," Tinbergen Institute Discussion Papers 05-003/4, Tinbergen Institute.
    8. Cecchin, Alekos & Pelino, Guglielmo, 2019. "Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4510-4555.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:152:y:2022:i:c:p:533-559. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.