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Renewal Contact Processes: Phase transition and survival

Author

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  • 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
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    References listed on IDEAS

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    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.
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