Branching processes in random environment which extinct at a given moment

الأصل · EN

Let Zₙ,n≥ 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→ ∞, 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 Znt,δ≤ t≤ 1-δ given T=n+1 and δ∈ (0,1/2).