Contact process under renewals II

Author(s)

Fontes, Luiz Renato ^[1] ; Mountford, Thomas S. ^[2] ; Vares, Maria Eulalia ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

^[2] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne - Switzerland

^[3] Univ Fed Rio de Janeiro, Inst Matemat, Rio De Janeiro, RJ - Brazil

• Document type: Journal article
• Source: Stochastic Processes and their Applications; v. 130, n. 2, p. 1103-1118, FEB 2020.
• Web of Science Citations: 0

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 mu is heavier than t(-alpha) for some alpha < 1 (plus auxiliary regularity conditions) then the critical value vanishes. In this paper we show that if mu has decreasing hazard rate and tail bounded by t(-alpha) with alpha > 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. (C) 2019 Published by Elsevier B.V. (AU)

• FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants