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Times of a branching process with immigration in varying environment attaining a fixed level
- Publication Year :
- 2023
-
Abstract
- Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a criterion to determine whether the set $C$ is finite or not. For critical Galton-Watson process, we show that $|C\cap [1,n]|/\log n\rightarrow S$ in distribution, where $S$ is an exponentially distributed random variable with $P(S>t)=e^{-t},\ t>0.$<br />Comment: 20 pages
- Subjects :
- Mathematics - Probability
60J80, 60J10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.03614
- Document Type :
- Working Paper