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Uniqueness and Decay Properties of Markov Branching Processes with Disasters

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Anyue Chen ,
Kai Wang Ng  and
Hanjun Zhang
Anyue Chen*
Affiliation:
South University of Science and Technology of China and University of Liverpool
Kai Wang Ng*
Affiliation:
University of Hong Kong
Hanjun Zhang*
Affiliation:
Xiangtan University
*
∗ Postal address: Department of Financial Mathematics and Financial Engineering, South University of Science and Technology of China, Shenzhen, Guangdong, 518055, P. R. China. Email address: chen.ay@sustc.edu.cn
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Email address: kaing@hku.hk
∗∗∗ Postal address: School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, P. R. China Email address: zhanghanjunxtu@gmail.com
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Abstract

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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 λC . We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λC -positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

Keywords

Markov branching processdisasterdecay parameterinvariant measureinvariant vectorquasistationary distribution

MSC classification

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

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 613 - 624
Copyright
© Applied Probability Trust 

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