Yaglom's limit for critical Galton-Watson processes in varying environment: A probabilistic approach

Abstract

A Galton-Watson process in varying environment is a discrete time branching process where the offspring distributions vary among generations. Based on a twospine decomposition technique, we provide a probabilistic argument of a Yaglom-type limit for this family processes. The result states that, in the critical case, a suitable normalisation of the process conditioned on non-extinction converges in distribution to an exponential random variable. Recently, this result has been established by Kersting [J. Appl. Probab. 57(1), 196-220, 2020] using analytic techniques.