## View abstract

### Session S04 - Random Walks and Related Topics

Friday, July 16, 13:40 ~ 14:10 UTC-3

## On renewal contact processes: some new results

### Maria Eulália Vares

#### Instituto de Matemática / Universidade Federal do Rio de Janeiro, Brasil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak547a48f0f42e42a50b96d8ee7728b414').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy547a48f0f42e42a50b96d8ee7728b414 = '&#101;&#117;l&#97;l&#105;&#97;' + '&#64;'; addy547a48f0f42e42a50b96d8ee7728b414 = addy547a48f0f42e42a50b96d8ee7728b414 + '&#105;m' + '&#46;' + '&#117;frj' + '&#46;' + 'br'; var addy_text547a48f0f42e42a50b96d8ee7728b414 = '&#101;&#117;l&#97;l&#105;&#97;' + '&#64;' + '&#105;m' + '&#46;' + '&#117;frj' + '&#46;' + 'br';document.getElementById('cloak547a48f0f42e42a50b96d8ee7728b414').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy547a48f0f42e42a50b96d8ee7728b414 + '\'>'+addy_text547a48f0f42e42a50b96d8ee7728b414+'<\/a>';

This talk will be mostly based on [1]. We refine previous results concerning the renewal contact processes and significantly widen the family of interarrival times for which the critical value can be shown to be strictly positive. The result now holds for any spatial dimension $d\ge 1$ and the decreasing failure rate assumption present in [2] is removed, among other improvements. For heavy tailed interarrival times we provide some further description of the processes, including a complete convergence theorem and an examination of how, conditioned on survival, the process can be asymptotically predicted knowing the renewal processes.

[1] L.R. Fontes, T.S. Mountford, D. Ungaretti, M.E. Vares. Renewal contact processes: phase transition and survival (arXiv:2101.06207 [math.PR])

[2] L.R. Fontes, T.S. Mountford, M.E. Vares. Contact process under renewals II. Stoch. Proc. Appl., v. 130, p. 1103-1118, 2020.

Joint work with Luiz Renato Fontes (USP, Brazil), Thomas S. Mountford (EPFL, Switzerland), Daniel Ungaretti (USP, Brazil).