Uniqueness and extinction properties of generalised Markov branching processes

Submitted by U. Stadtmueller
https://doi.org/10.1016/S0022-247X(02)00251-2Get rights and content
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Abstract

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

Keywords

Markov branching processes (MBP)
Generalised Markov branching processes (GMBP)
Uniqueness
Differential–integral equation
Extinction probability
Mean extinction time
Conditional mean extinction time

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