Critical Galton-Watson branching processes with a countable set of types and infinite second moments

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Abstract

We consider an indecomposable Galton-Watson branching process with a countable set of types. Assuming that the process is critical and may have infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behaviour 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. Bibliography: 20 titles.

About the authors

Vladimir Alekseevich Vatutin

Steklov Mathematical Institute of Russian Academy of Sciences

Email: vatutin@mi-ras.ru
Doctor of physico-mathematical sciences, Professor

Elena Evgen'evna Dyakonova

Steklov Mathematical Institute of Russian Academy of Sciences

Email: elena@mi-ras.ru
Doctor of physico-mathematical sciences, Head Scientist Researcher

Valentin Alekseevich Topchii

Mathematical Center in Akademgorodok; Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: topchij@gmail.com
Doctor of physico-mathematical sciences, Professor

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