Critical branching processes in a sparse random environment
Volume 10, Issue 4 (2023), pp. 397–411
Pub. online: 29 August 2023
Type: Research Article
Open Access
Open Access
Received
11 June 2023
11 June 2023
Revised
31 July 2023
31 July 2023
Accepted
31 July 2023
31 July 2023
Published
29 August 2023
29 August 2023
Abstract
We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event.
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