Branching processes in random environment which extinct at a given moment

Abstract

Let $Z_n,n\ge 0$ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at moment $n$ given $T=n+1$ and a functional limit theorem for the properly scaled process $Z_{nt},\delta \le t\le 1-\delta$ given $T=n+1$ and $\delta \in (0,1/2)$.

21 pages; submitted to Markov Processes and Related Fields

References in corpus (1)

• Limit theorems for weakly subcritical branching processes in random environment

Cited by in corpus (3)

• Extinction rate of continuous state branching processes in critical Lévy environments
• Branching processes in a Lévy random environment
• Survival of branching processes in random environments