Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/589

 Title: On the Structure of Spatial Branching Processes Authors: Matthes, KlausNawrotzki, KurtSiegmund-Schultze, Rainer Keywords: Branching Particle SystemsTwo-Sided Infinite Markov Sequences of a Random PopulationsGenealogyPoisson 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. URI: http://hdl.handle.net/10525/589 ISSN: 1310-6600 Appears in Collections: Volume 23 Number 3-4

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