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

Natalia Cardona-Tobón; Sandra Palau

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arXiv · 2005.10186

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

Natalia Cardona-Tobón·Sandra Palau

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Abstract

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 an exponential random variable. Recently, this result has been established by Kersting [{\it J. Appl. Probab.} {\bf57}(1), 196--220, 2020] using analytic techniques.

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Natalia Cardona-Tobón, Sandra Palau. 2020-05-20. Yaglom's limit for critical Galton-Watson processes in varying environment: A probabilistic approach. https://arxiv.org/abs/2005.10186

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