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Contact process under renewals I

Author

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  • Fontes, Luiz Renato G.
  • Marchetti, Domingos H.U.
  • Mountford, Thomas S.
  • Vares, Maria Eulalia

Abstract

We investigate a non-Markovian analogue of the Harris contact process in Zd: an individual is attached to each site x∈Zd, and it can be infected or healthy; the infection propagates to healthy neighbours just as in the usual contact process, according to independent exponential times with a fixed rate λ; nevertheless, the possible recovery times for an individual are given by the points of a renewal process with heavy tail; the renewal processes are assumed to be independent for different sites. We show that the resulting processes have a critical value equal to zero.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:8:p:2903-2911
    DOI: 10.1016/j.spa.2018.08.007
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    Cited by:

    1. 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.
    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. Jiang, Zhimin & Cai, Jie & Moses, Paul S., 2020. "Smoothing control of solar photovoltaic generation using building thermal loads," Applied Energy, Elsevier, vol. 277(C).
    4. 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.
    5. 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).

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