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Critical Bellman-Harris branching processes starting from a large number of particles. (Russian) Zbl 0621.60092
A standard critical age-dependent branching process z(t,N) is considered, where \(z(0,N)=N\). Limit distributions of \(\psi\) (t)z(t,N(t)), as t tends to infinity, are investigated under the general hypothesis N(t)\(\to \infty\), with \(\psi\) (t) properly selected.
Four theorems are stated and proved. The limit properties depend, among others, on the variability of G(t) (particle lifelength distribution) at infinity and on the variability of f(x) (generating function of progeny number) at \(x=1\). Limit distributions are provided either explicitly or as the solutions of functional equations.
Reviewer: M.Kimmel

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)