Variance estimators in critical branching processes with non-homogeneous immigration

TL;DR

This paper establishes the asymptotic normality of estimators for offspring variance in critical branching processes with non-homogeneous immigration, using martingale techniques and weak convergence methods.

Contribution

It provides new theoretical results on the asymptotic behavior of variance estimators in complex branching processes with non-constant immigration.

Findings

Asymptotic normality of estimators proven

Applicable under moment conditions on reproduction and immigration

Uses martingale and weak convergence techniques

Abstract

The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The proofs use martingale techniques and weak convergence results in Skorokhod spaces.