Vol. 3, No. 4, 2021

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Central limit theorem for a critical multitype branching process in random environments

Emile Le Page, Marc Peigné and Da Cam Pham

Vol. 3 (2021), No. 4, 801–842
Abstract

Let (Zn)n0 with Zn = (Zn(i,j))1i,jp be a p multitype critical branching process in random environment, and let Mn be the expectation of Zn given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes {(Zn|Mn|)|Zn| > 0} and {(lnZnn)|Zn| > 0}. These theorems extend similar results for single-type critical branching process in random environments.

Emile Le Page passed away on May 2021, after a lengthy battle with cancer. We have lost a generous colleague and a friend. — Marc Peigné and Da Cam Pham

Keywords
multitype branching process, random environment, central limit theorem
Mathematical Subject Classification
Primary: 60J80, 60K37
Secondary: 60F17
Milestones
Received: 10 September 2020
Revised: 26 October 2020
Accepted: 21 November 2020
Published: 20 October 2021
Authors
Emile Le Page
Université de Bretagne-Sud
LMBA UMR CNRS 6205
Vannes
France
Marc Peigné
Institut Denis Poisson UMR 7013
Université de Tours
France
Da Cam Pham
ESAIP École d’Ingénieurs
St. Barthélémy d’Anjou
France