IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i10p3077-3101.html
   My bibliography  Save this article

Long time behavior of telegraph processes under convex potentials

Author

Listed:
  • Fontbona, Joaquin
  • Guérin, Hélène
  • Malrieu, Florent

Abstract

We study the long-time behavior of variants of the telegraph process with position-dependent jump-rates, which result in a monotone gradient-like drift towards the origin. We compute their invariant laws and obtain, via probabilistic couplings arguments, some quantitative estimates of the total variation distance to equilibrium. Our techniques extend ideas previously developed for a simplified piecewise deterministic Markov model of bacterial chemotaxis.

Suggested Citation

  • Fontbona, Joaquin & Guérin, Hélène & Malrieu, Florent, 2016. "Long time behavior of telegraph processes under convex potentials," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3077-3101.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3077-3101
    DOI: 10.1016/j.spa.2016.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916300242
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.04.002?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. Chafaï, Djalil & Malrieu, Florent & Paroux, Katy, 2010. "On the long time behavior of the TCP window size process," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1518-1534, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nikita Ratanov, 2020. "First Crossing Times of Telegraph Processes with Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 349-370, March.
    2. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.

    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. Brandejsky, Adrien & de Saporta, Benoîte & Dufour, François, 2013. "Optimal stopping for partially observed piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3201-3238.
    2. Montagnon, Pierre, 2020. "Stability of piecewise deterministic Markovian metapopulation processes on networks," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1515-1544.
    3. Denis Villemonais, 2020. "Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes," Journal of Theoretical Probability, Springer, vol. 33(2), pages 954-991, June.

    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:126:y:2016:i:10:p:3077-3101. 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.