Markov branching processes with regularly varying generating function and immigration of a special form. (Russian, English) Zbl 1026.60099

Formanov, Sh. K.; Azimov, Zh. B.

Teor. Jmovirn. Mat. Stat. 65, 161-167 (2001); translation in Theory Probab. Math. Stat. 65, 181-188 (2002).

The asymptotic behaviour of the critical Markov branching processes with immigration which depends on the state “0” is investigated under the assumption that the generating function has an infinite second moment but regularly varying in the neighborhood of the state “1”. The proofs of the proposed theorems are based on the renewal theory and asymptotic properties of regularly varying functions.

Reviewer: Mikhail Moklyachuk (Kyïv)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)

Keywords:

Markov branching processes; immigration critical asymptotic behaviour; infinite second moment; regularly varying function