On the Structure of Spatial Branching Processes

Matthes, Klaus, Nawrotzki, Kurt, and Siegmund-Schultze, Rainer. "On the Structure of Spatial Branching Processes." Serdica Mathematical Journal 23.3-4 (1997): 269-312. <http://eudml.org/doc/11619>.

@article{Matthes1997,
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.},
author = {Matthes, Klaus, Nawrotzki, Kurt, Siegmund-Schultze, Rainer},
journal = {Serdica Mathematical Journal},
keywords = {Branching Particle Systems; Two-Sided Infinite Markov Sequences of a Random Populations; Genealogy; Poisson Distribution; branching particle system; two-sided infinite Markov sequences of a random population; genealogy; Poisson distribution},
language = {eng},
number = {3-4},
pages = {269-312},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Structure of Spatial Branching Processes},
url = {http://eudml.org/doc/11619},
volume = {23},
year = {1997},
}

TY - JOUR
AU - Matthes, Klaus
AU - Nawrotzki, Kurt
AU - Siegmund-Schultze, Rainer
TI - On the Structure of Spatial Branching Processes
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 3-4
SP - 269
EP - 312
AB - 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.
LA - eng
KW - Branching Particle Systems; Two-Sided Infinite Markov Sequences of a Random Populations; Genealogy; Poisson Distribution; branching particle system; two-sided infinite Markov sequences of a random population; genealogy; Poisson distribution
UR - http://eudml.org/doc/11619
ER -