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On the Structure of Spatial Branching Processes

Matthes, Klaus;  Nawrotzki, Kurt;  Siegmund-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...

Universally typical sets for ergodic sources of multidimensional data

Tyll Krüger;  Guido F. Montúfar;  Ruedi Seiler;  Rainer Siegmund-Schultze — 2013

Kybernetika

We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an h 0 with...

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