On the eve property for CSBP. (English) Zbl 1287.60100

Duquesne, Thomas; Labbé, Cyril

Electron. J. Probab. 19, Paper No. 6, 31 p. (2014).

Summary: We consider the population model associated to continuous state branching processes and we are interested in the so-called Eve property that asserts the existence of an ancestor with an overwhelming progeny at large times, and more generally, in the possible behaviours of the frequencies among the population at large times. In this paper, we classify all the possible behaviours according to the branching mechanism of the continuous state branching process.

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60E07	Infinitely divisible distributions; stable distributions
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

continuous state branching process; Eve; dust; Grey martingale; frequency distribution