The multiple birth properties of multi-type Markov branching processes

TL;DR

This paper introduces a new multi-dimensional Markov process to analyze the multiple birth properties of multi-type Markov branching processes, providing joint and extinction time distributions.

Contribution

It constructs a novel process that captures multiple birth characteristics and derives their joint and extinction distributions.

Findings

Joint distribution of multiple births until time t derived

Distribution of multiple births until extinction obtained

New process reveals birth characteristics in multi-type processes

Abstract

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time $t$ is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.