Back to Search
Start Over
Null recurrence and transience for a binomial catastrophe model in random environment
- Publication Year :
- 2022
-
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). 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.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2211.14193
- Document Type :
- Working Paper