On Supercritical Branching Processes with Emigration

TL;DR

This paper investigates supercritical branching processes with independent emigration, establishing conditions for finite lifetime and expectation, presenting a new Kesten-Stigum theorem, and linking extinction probability to emigration tail behavior.

Contribution

It introduces a novel version of the Kesten-Stigum theorem for processes with emigration and analyzes extinction probabilities related to emigration tail behavior.

Findings

Conditions for finite process lifetime and expectation

A new Kesten-Stigum theorem for emigration-influenced processes

Extinction probability linked to emigration tail behavior

Abstract

We study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the Kesten-Stigum theorem is obtained and the extinction probability for a large initial population size is related to the tail behaviour of the emigration.