An averaging principle for near-critical branching processes with semi-Markov switchings. (English. Ukrainian original) Zbl 0948.60075

Anisimov, V. V.

Theory Probab. Math. Stat. 52, 13-26 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 13-25 (1995).

The author introduces the notion of branching processes with continuous time and semi-Markov switchings. Under the condition where these processes approach the critical ones, a uniform convergence in probability of normed sample paths to the unique solution of an ordinary differential equation is proved.

Reviewer: O.K.Zakusilo (Kyïv)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60K15	Markov renewal processes, semi-Markov processes
60F17	Functional limit theorems; invariance principles

Keywords:

branching process; convergence in probability; sample paths