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Uniqueness and decay properties of Markov branching processes with disasters. (English) Zbl 1305.60084

Summary: In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding \(q\)-matrix \(Q\) is always regular and thus that the Feller minimal \(Q\)-process is honest, we obtain the exact value of the decay parameter \(\lambda_C\). We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always \(\lambda_{C}\)-positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J27 Continuous-time Markov processes on discrete state spaces
60J35 Transition functions, generators and resolvents
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References:

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