# On the Structure of Spatial Branching Processes

Matthes, Klaus; Nawrotzki, Kurt; Siegmund-Schultze, Rainer

Serdica Mathematical Journal (1997)

- Volume: 23, Issue: 3-4, page 269-312
- ISSN: 1310-6600

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topMatthes, 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 -

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