Branching processes in random environment which extinct at a given moment

Details Branching processes in random environment which extinct at a given moment Branching processes in random environment which extinct at a given moment

2010-01-14

arxiv.org/abs/1001.2413v1

Markov Process. Related Fields 16 (2010), no. 2, 329-350

Mathematics

Probability

21 pages; submitted to Markov Processes and Related Fields

Scientific paper

Let ${Z_{n},n\geq 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 \leq t\leq 1-\delta} $ given $T=n+1$ and $\delta \in (0,1/2)$.

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