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  6. Volume 23 Number 3-4
  7. On the Structure of Spatial Branching Processes

On the Structure of Spatial Branching Processes

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Authors: Matthes, KlausNawrotzki, KurtSiegmund-Schultze, Rainer
Issue Date: 1997
Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 269p-312p Copy to clipboard
ISSN: 1310-6600
URI: http://hdl.handle.net/10525/589 Copy to clipboard
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.
Language: en
Publisher: Institute of Mathematics and Informatics, Bulgarian Academy of SciencesSubject: Branching Particle SystemsTwo-Sided Infinite Markov Sequences of a Random PopulationsGenealogyPoisson Distribution
Type: Article