Yaglom’s limit for critical Galton–Watson processes in varying environment: A probabilistic approach

A Galton–Watson process in varying environment is a discrete time branching process where the offspring distributions vary among generations. Based on a two-spine 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 a standard exponential random variable.