Decay Properties of n-type Markov Branching Processes with Disasters

Wei Wei Meng () and Jun Ping Li ()
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Wei Wei Meng: Central South University
Jun Ping Li: Central South University

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1605-1623

Abstract: Abstract In this paper, we consider the decay properties of n-type Markov branching processes with disasters, including the decay parameter and invariant measures. It is first proved that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest. Then, the exact value of the decay parameter $$\lambda _C$$ λ C is obtained. We prove that the decay parameter can be easily expressed explicitly. Furthermore, we prove that the Markov branching process with disasters is always $$\lambda _C$$ λ C -positive. The invariant vectors and the invariant measures are given explicitly.

Keywords: n-type Markov branching process with disasters; Decay parameter; Invariant measures; Invariant vectors; 60J27; 60J35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0681-9

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