The asymptotic behavior of critical branching processes with immigration at zero. (English. Ukrainian original) Zbl 0948.60076

Bojko, R. V.

Theory Probab. Math. Stat. 52, 27-32 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 26-31 (1995).

The paper deals with branching processes \(\eta (t)\) that admit immigration at zero. It is assumed that immigration has infinite mean value. Theorem 1 gives conditions for \(P_{00}(t) = P\{\eta(t)=0\mid\eta(0)=0\}\) to be regularly varying at infinity. The limiting behavior of \(\eta (t)\) itself is investigated.

Reviewer: O.K.Zakusilo (Kyïv)

MSC:

60J80

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

Keywords:

branching process; asymptotic behavior