| Abstract: | 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 A. M. Zubkov, obtained for Markov branching processes. For the proof one makes use in an essential manner of the known inequalities of Goldstein, estimating the generating function of the Bellman-Harris process in terms of the generating functions of the imbedded Galton-Watson process.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 60–82, 1986. |
