[Développements du premier et du second ordre dans le théorème central limite pour une marche aléatoire avec branchement]
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.
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.
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@article{CRMATH_2016__354_5_532_0,
author = {Gao, Zhiqiang and Liu, Quansheng},
title = {First- and second-order expansions in the central limit theorem for a branching random walk},
journal = {Comptes Rendus. Math\'ematique},
pages = {532--537},
publisher = {Elsevier},
volume = {354},
number = {5},
year = {2016},
doi = {10.1016/j.crma.2016.01.021},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.01.021/}
}
TY - JOUR AU - Gao, Zhiqiang AU - Liu, Quansheng TI - First- and second-order expansions in the central limit theorem for a branching random walk JO - Comptes Rendus. Mathématique PY - 2016 SP - 532 EP - 537 VL - 354 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.01.021/ DO - 10.1016/j.crma.2016.01.021 LA - en ID - CRMATH_2016__354_5_532_0 ER -
%0 Journal Article %A Gao, Zhiqiang %A Liu, Quansheng %T First- and second-order expansions in the central limit theorem for a branching random walk %J Comptes Rendus. Mathématique %D 2016 %P 532-537 %V 354 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.01.021/ %R 10.1016/j.crma.2016.01.021 %G en %F CRMATH_2016__354_5_532_0
Gao, Zhiqiang; Liu, Quansheng. First- and second-order expansions in the central limit theorem for a branching random walk. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 532-537. doi : 10.1016/j.crma.2016.01.021. http://archive.numdam.org/articles/10.1016/j.crma.2016.01.021/
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