A conceptual proof of the Kesten-Stigum theorem for multi-type branching processes. (English) Zbl 0868.60068

Kurtz, Thomas; Lyons, Russell; Pemantle, Robin; Peres, Yuval

Athreya, Krishna B. (ed.) et al., Classical and modern branching processes. Proceedings of the IMA workshop, Minneapolis, MN, USA, June 13–17, 1994. New York, NY: Springer. IMA Vol. Math. Appl. 84, 181-185 (1997).

A probabilistic proof of the Kesten-Stigum theorem for multitype branching processes is given through the first author’s unpublished theorem of convergence of types (its proof is also included in the paper) and the last three authors’ method of proof for single-type case [Ann. Probab. 23, No. 3, 1125-1138 (1995; Zbl 0840.60077)].
For the entire collection see [Zbl 0855.00027].

Reviewer: He Sheng Wu (Shanghai)

MSC:

60J80

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

Keywords:

Galton-Watson process; size-biased distribution

Citations:

Zbl 0840.60077