Tail generating functions for Markov branching processes

TL;DR

This paper introduces a novel tail generating function approach to analyze one-type Markov branching processes, providing new limit theorems and streamlined proofs focused on the singularity points of the generating functions.

Contribution

It presents a concise, self-contained method for deriving limit theorems in Markov branching processes using tail generating functions, offering new insights and simplified proofs.

Findings

New limit theorems for Markov branching processes

Streamlined proofs based on tail generating functions

Analysis centered on singularity points of generating functions

Abstract

We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our analysis focuses on the singularity points of the master integral equation for the probability generating functions of the current population size.