Displaying similar documents to “Spatial birth-and-dead processes in random environment.”

On the Structure of Spatial Branching Processes

Matthes, Klaus, Nawrotzki, Kurt, Siegmund-Schultze, Rainer (1997)

Serdica Mathematical Journal

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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...

Coupling a branching process to an infinite dimensional epidemic process

Andrew D. Barbour (2010)

ESAIM: Probability and Statistics

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Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection,...