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Contact process under renewals II

Author

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  • Fontes, Luiz Renato
  • Mountford, Thomas S.
  • Vares, Maria Eulália

Abstract

We continue the study of renewal contact processes initiated in a companion paper, where we showed that if the tail of the interarrival distribution μ is heavier than t−α for some α<1 (plus auxiliary regularity conditions) then the critical value vanishes. In this paper we show that if μ has decreasing hazard rate and tail bounded by t−α with α>1, then the critical value is positive in the one-dimensional case. A more robust and much simpler argument shows that the critical value is positive in any dimension whenever the interarrival distribution has a finite second moment.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:1103-1118
    DOI: 10.1016/j.spa.2019.04.008
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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.
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    Cited by:

    1. 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.

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