A unifying approach to branching processes in varying environments

2017/03/06 by Götz Kersting, Kersting, Götz · 2 citations
Computer Science · Mathematics · #60J80 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Bayesian Inference #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1703.01960

openalex publication_date 2017/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Branching processes (Z_n)_{n ≥ 0} in a varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results concern general criteria for a.s. extinction, square-integrability of the martingale (Z_n/\mathbf E[Z_n])_{n ≥ 0}, properties of the martingale limit W and a Yaglom type result stating convergence to an exponential limit distribution of the suitably normalized population size Z_n, conditioned on the event Z_n >0. The theorems generalize/unify diverse results from the literature and lead to a classification of the processes.

Citations

• Time-Inhomogeneous Branching Processes Conditioned on Non-Extinction

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