First- and second-order expansions in the central limit theorem for a branching random walk

Zhiqiang Gao; Quansheng Liu

doi:10.1016/j.crma.2016.01.021

Probability theory

First- and second-order expansions in the central limit theorem for a branching random walk

Presented by: Jean-Pierre Kahane

Zhiqiang Gao ¹; Quansheng Liu ^2,³

¹ School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, PR China
² Univ. Bretagne-Sud, CNRS UMR 6205, LMBA, campus de Tohannic, 56000 Vannes, France
³ Changsha University of Science and Technology, School of Mathematics and Statistics, Changsha 410004, China

Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 532-537.

Abstract
Résumé

We give the first- and second-order asymptotic expansions for the central limit theorem about the distribution of particles in a branching random walk on the real line. In particular, our first-order expansion reveals the exact convergence rate in the central limit theorem; it extends and improves a known result for the branching Wiener process.

Nous donnons les développements asymptotiques d'ordres un et deux dans le théorème central limite sur la distribution des particules dans une marche aléatoire avec branchement sur la droite réelle. En particulier, le développement asymptotique d'ordre un révèle la vitesse exacte de convergence du théorème central limite, ce qui étend et améliore un résultat connu pour le processus de Wiener avec branchement.

Received: 2015-09-02
Accepted: 2016-01-25
Published online: 2016-04-19

DOI: 10.1016/j.crma.2016.01.021

Author's affiliations:

Zhiqiang Gao ¹; Quansheng Liu ^{2, 3}

¹ School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, PR China
² Univ. Bretagne-Sud, CNRS UMR 6205, LMBA, campus de Tohannic, 56000 Vannes, France
³ Changsha University of Science and Technology, School of Mathematics and Statistics, Changsha 410004, China

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     author = {Zhiqiang Gao and Quansheng Liu},
     title = {First- and second-order expansions in the central limit theorem for a branching random walk},
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     language = {en},
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Zhiqiang Gao; Quansheng Liu. First- and second-order expansions in the central limit theorem for a branching random walk. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 532-537. doi : 10.1016/j.crma.2016.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.021/

References
Cited by

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