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

Let ${(Z_{n})}_{n \geq 0}$ with $Z_{n} = {(Z_{n} (i, j))}_{1 \leq i, j \leq p}$ be a $p$ multitype critical branching process in random environment, and let $M_{n}$ be the expectation of $Z_{n}$ given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes ${(Z_{n} ∕ | M_{n} |) ∣ | Z_{n} | > 0}$ and ${(ln Z_{n} ∕ \sqrt{n}) ∣ | Z_{n} | > 0}$ . 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

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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

Vol. 3, No. 4, 2021

Emile Le Page, Marc Peigné and Da Cam Pham

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors