an:04094539
Zbl 0668.60076
Badalbaev, I. S.; Mashrabbaev, A.
The life spans of a Bellman-Harris branching process with immigration
EN
J. Sov. Math. 38, No. 5, 2198-2210 (1987); translation from Probability distributions and mathematical statistics, Collect. Artic., Tashkent 1986, 60-82 (1986).
00181437
1987
j
60J80
Bellman-Harris process with immigration; Galton-Watson process
[For the entire collection see Zbl 0626.00025.]
One considers two schemes of the Bellman-Harris process with immigration when
a) the lifetime of the particles is an integral-valued random variable and the immigration is defined by a sequence of independent random variables;
b) the distribution of the lifetime of the particles is nonlattice and the immigration is a process with continuous time.
One investigates the properties of the life spans of such processes. The results obtained here are a generalization to the case of Bellman-Harris processes of the results of \textit{A. M. Zubkov} [Theory Probab. Appl. 17, 174-183 (1972; Zbl 0267.60084); translation from Teor. Veroyatn. Primen. 17, 179-188 (1972)] obtained for Markov branching processes. For the proof one makes use in an essential manner of the well-known Goldstein inequalities estimating the generating function of the Bellman-Harris process in terms of the generating functions of the imbedded Galton- Watson process.
Zbl 0626.00025; Zbl 0267.60084