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Arbres et processus de Bellman-Harris. (Trees and Bellman-Harris processes). (French) Zbl 0597.60078
An analog of the branching law of Galton-Watson processes is given for a supercritical Bellman-Harris process by using a tree representation [see A. Joffe, Adv. Probab. Relat. Top., Vol. 5, 263-267 (1978; Zbl 0414.60078)].
As in the paper by J. Neveu, Arbres et processus de Galton-Watson. Ann. Inst. Henri Poincaré, Probab. Stat. 22, 199-208 (1986), one first considers the probability space of trees and a ”stopping line”. The translated trees are independent and possess the same probability law (Proposition 1), the trees being disjoint - which is in agreement with the definition of the stopping line. A renormalized Markov semigroup is defined (Proposition 5) and results on the \(L^ 2\)-convergence of the process, age distribution and renewal theorem are obtained.
Reviewer: P.Tautu

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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