Yaglom’s limit for Galton-Watson processes in varying environment
A Galton–Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. In this talk, we will discuss Yaglom-type limit for such family of processes. The result states that, in the critical regime, a suitable normalisation of the process conditioned on non-extinction converges in distribution to a standard exponential random variable. We provide a proof is based on a two-spine decomposition technique. Moreover, we will discuss the rate of convergence of the Yaglom limit with respect to the Wasserstein metric.