Branching processes in nearly degenerate varying environment

Kevei, Péter and Kubatovics, Kata (2024) Branching processes in nearly degenerate varying environment. Journal of Applied Probability. ISSN 0021-9002 (In Press)

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Abstract

We investigate branching processes in varying environment. Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on non-extinction, and adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting.

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