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August 2021 Yaglom’s limit for critical Galton–Watson processes in varying environment: A probabilistic approach
Natalia Cardona-Tobón, Sandra Palau
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Bernoulli 27(3): 1643-1665 (August 2021). DOI: 10.3150/20-BEJ1286

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 a standard exponential random variable.

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Natalia Cardona-Tobón. Sandra Palau. "Yaglom’s limit for critical Galton–Watson processes in varying environment: A probabilistic approach." Bernoulli 27 (3) 1643 - 1665, August 2021. https://doi.org/10.3150/20-BEJ1286

Information

Received: 1 May 2020; Revised: 1 August 2020; Published: August 2021
First available in Project Euclid: 10 May 2021

Digital Object Identifier: 10.3150/20-BEJ1286

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 3 • August 2021
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