IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v161y2023icp102-136.html
   My bibliography  Save this article

Renewal Contact Processes: Phase transition and survival

Author

Listed:
  • Fontes, Luiz Renato
  • Mountford, Thomas S.
  • Ungaretti, Daniel
  • Vares, Maria Eulália

Abstract

We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for any dimension d≥1 and requires only a moment condition slightly stronger than finite first moment. For heavy-tailed interarrival times, we prove a Complete Convergence Theorem and examine when the contact process, conditioned on survival, can be asymptotically predicted knowing the renewal processes. We close with an example of distribution attracted to a stable law of index 1 for which the critical value vanishes.

Suggested Citation

  • Fontes, Luiz Renato & Mountford, Thomas S. & Ungaretti, Daniel & Vares, Maria Eulália, 2023. "Renewal Contact Processes: Phase transition and survival," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 102-136.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:102-136
    DOI: 10.1016/j.spa.2023.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923000509
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.03.005?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. Fontes, Luiz Renato G. & Marchetti, Domingos H.U. & Mountford, Thomas S. & Vares, Maria Eulalia, 2019. "Contact process under renewals I," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2903-2911.
    2. Fontes, Luiz Renato & Mountford, Thomas S. & Vares, Maria Eulália, 2020. "Contact process under renewals II," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1103-1118.
    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. Jiang, Zhimin & Cai, Jie & Moses, Paul S., 2020. "Smoothing control of solar photovoltaic generation using building thermal loads," Applied Energy, Elsevier, vol. 277(C).
    2. Nguyen, Hieu T. & Felder, Frank A., 2020. "Generation expansion planning with renewable energy credit markets: A bilevel programming approach," Applied Energy, Elsevier, vol. 276(C).
    3. Fontes, Luiz Renato & Mountford, Thomas S. & Vares, Maria Eulália, 2020. "Contact process under renewals II," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1103-1118.
    4. Chudinzow, Dimitrij & Nagel, Sylvio & Güsewell, Joshua & Eltrop, Ludger, 2020. "Vertical bifacial photovoltaics – A complementary technology for the European electricity supply?," Applied Energy, Elsevier, vol. 264(C).

    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:161:y:2023:i:c:p:102-136. 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.