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On the Structure of Spatial Branching Processes

Matthes, KlausNawrotzki, KurtSiegmund-Schultze, Rainer — 1997

Serdica Mathematical Journal

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...

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