Rates on Yaglom's limit for Galton-Watson processes in a varying environment

Abstract

A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable normalization of the process conditioned on non-extinction converges in distribution to a standard exponential random variable. In this manuscript, we provide the rate of convergence of the Yaglom limit with respect to the Wasserstein metric.

22 pages. Corrected some minor errors in the introduction, specifically in Theorem 1.2 and Equation 1.3. Added new references