Decay Properties of n-type Markov Branching Processes with Disasters

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 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 λ C -positive. The invariant vectors and the invariant measures are given explicitly.