Regularly varying nonstationary second-order Galton-Watson processes with immigration

TL;DR

This paper establishes conditions under which nonstationary second-order Galton-Watson processes with immigration exhibit regular variation, enhancing understanding of their tail behavior in stochastic modeling.

Contribution

It provides new sufficient conditions for regular variation in nonstationary second-order Galton-Watson processes with immigration.

Findings

Identifies conditions for regular variation.

Analyzes tail behavior of the process.

Extends previous results to nonstationary cases.

Abstract

We give sufficient conditions on the offspring, the initial and the immigration distributions under which a second-order Galton-Watson process with immigration is regularly varying.