Null recurrence and transience for a binomial catastrophe model in random environment

Author(s)

Fontes, Luiz Renato ; Machado, Fabio P. ; Schinazi, Rinaldo B.

• Document type: Journal article
• Source: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. 2023, n. 3, p. 17-pg., 2023-03-01.

Abstract

We consider a discrete time population model for which each individual alive at time n survives independently of everybody else at time n + 1 with probability beta(n). The sequence (beta(n)) is i.i.d. and constitutes our random environment. Moreover, at every time n we add Z(n) individuals to the population. The sequence (Z(n)) is also i.i.d. We find sufficient conditions for null recurrence and transience (positive recurrence has been addressed by Neuts 1994 J. Appl. Probab. 31 48-58). We apply our results to a particular (Z(n)) distribution and deterministic beta. This particular case shows a rather unusual phase transition in beta in the sense that the Markov chain goes from transience to null recurrence without ever reaching positive recurrence. (AU)

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