Branching Particle Systems Two-Sided Infinite Markov Sequences of a Random Populations Genealogy Poisson Distribution
Issue Date:
1997
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 269p-312p
Abstract:
The paper is a contribution to the theory of branching processes
with discrete time and a general phase space in the sense of [2]. We
characterize the class of regular, i.e. in a sense sufficiently random, branching
processes (Φk) k∈Z by almost sure properties of their realizations without
making any assumptions about stationarity or existence of moments.
This enables us to classify the clans of (Φk) into the regular part and the
completely non-regular part. It turns out that the completely non-regular
branching processes are built up from single-line processes, whereas the
regular ones are mixtures of left-tail trivial processes with a Poisson family
structure.
