Critical Galton-Watson branching processes with countably infinitely many types and infinite second moments

2020/02/28 by V. A. Topchiī, Vladimir Vatutin, Topchii, V. A. +3
Mathematics · Physics and Astronomy · #60J80 (Primary) 15B48 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2002.12627

openalex publication_date 2020/02/28 · openalex created_date 2020/03/06 · openalex updated_date 2026/07/28

Abstract

We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behavior of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types.

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