Branching Bellman-Harris processes. (Ветвящиеся процессы Беллмана-Харриса.) (Russian) Zbl 1304.60007

Vatutin, V. A.

Lektsionnye Kursy NOTs 12. Moskva: Matematicheskiĭ Institut im. V. A. Steklova, RAN (ISBN 5-98419-031-1/pbk). 111 p. (2009).

This work represents a lecture course on Branching Bellman-Harris processes. Let \(Z(t)\) be a number of particles in Bellman-Harris processes at moment \(t\). The main theme of this course is the study of so-called nonregular processes. The branching Bellman-Harris process is called nonregular if there exists a moment \(t<\infty\) such that \(\operatorname{P}(Z(t)<\infty)=1\). Finally, the author discusses the Crump-Mode process.

Reviewer: N. G. Gamkrelidze (Moskva)

MSC:

60-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J05	Discrete-time Markov processes on general state spaces

Keywords:

branching Bellman-Harris process; Crump-Mode-Jagers process