IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v188y2025ics0304414925001097.html
   My bibliography  Save this article

Stationary entrance chains and applications to random walks

Author

Listed:
  • Mijatović, Aleksandar
  • Vysotsky, Vladislav

Abstract

For a Markov chain Y with values in a Polish space, consider the entrance chain obtained by sampling Y at the moments when it enters a fixed set A from its complement Ac. Similarly, consider the exit chain, obtained by sampling Y at the exit times from Ac to A. We use the method of inducing from ergodic theory to study invariant measures of these two types of Markov chains in the case when the initial chain Y has a known invariant measure. We give explicit formulas for invariant measures of the entrance and exit chains under certain recurrence-type assumptions on A and Ac, which apply even for transient chains. Then we study uniqueness and ergodicity of these invariant measures assuming that Y is topologically recurrent, topologically irreducible, and weak Feller.

Suggested Citation

  • Mijatović, Aleksandar & Vysotsky, Vladislav, 2025. "Stationary entrance chains and applications to random walks," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001097
    DOI: 10.1016/j.spa.2025.104668
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104668?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Mijatović, Aleksandar & Uribe Bravo, Gerónimo, 2022. "Limit theorems for local times and applications to SDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 39-56.
    2. Vysotsky, Vladislav, 2010. "On the probability that integrated random walks stay positive," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1178-1193, July.
    3. Alexander Bendikov & Wojciech Cygan, 2015. "On massive sets for subordinated random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 288(8-9), pages 841-853, June.
    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. Chang-Song Deng, 2020. "Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination," Journal of Theoretical Probability, Springer, vol. 33(1), pages 522-532, March.
    2. Wojciech Cygan & Stjepan Šebek, 2021. "Transition probability estimates for subordinate random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 518-558, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:188:y:2025:i:c:s0304414925001097. 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.