Regularly varying non-stationary Galton--Watson processes with immigration

TL;DR

This paper establishes conditions under which non-stationary Galton--Watson processes with immigration exhibit regularly varying distributions at fixed times, enhancing understanding of their tail behavior.

Contribution

It provides new sufficient conditions for regular variation in non-stationary Galton--Watson processes with immigration, extending previous stationary results.

Findings

Identifies conditions for regular variation at fixed times.

Applies to processes with non-stationary initial, offspring, and immigration distributions.

Enhances understanding of tail behavior in complex stochastic processes.

Abstract

We give sufficient conditions on the initial, offspring and immigration distributions under which the distribution of a not necessarily stationary Galton--Watson process with immigration is regularly varying at any fixed time.