no. 6
Probabilités
A Berry–Esseen bound of order 1 n for martingales
[Une borne de Berry–Esseen d’ordre 1 n pour les martingales]
Wu, Songqi1 ; Ma, Xiaohui1 ; Sang, Hailin2 ; Fan, Xiequan1 
1 Center for Applied Mathematics, Tianjin University, Tianjin, China
2 Department of Mathematics, The University of Mississippi, University, MS 38677, USA
Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 701-712

Renz [13] has established a rate of convergence 1/n in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the methods, developed by Bolthausen [2] and Grama and Haeusler [6], is applied for obtaining the same convergence rate for a class of more general martingales. An application to linear processes is discussed.

Renz [13] a établi un taux de convergence 1/n dans le théorème de la limite centrale pour les martingales avec certaines conditions restrictives. Dans le présent article, une modification des méthodes, développées par Bolthausen [2] et Grama et Haeusler [6], est appliquée pour obtenir le même taux de convergence pour une classe de martingales plus générales. Une application aux processus linéaires est discutée.

Reçu le :
Accepté le :
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DOI : 10.5802/crmath.81

Wu, Songqi 1 ; Ma, Xiaohui 1 ; Sang, Hailin 2 ; Fan, Xiequan 1

1 Center for Applied Mathematics, Tianjin University, Tianjin, China
2 Department of Mathematics, The University of Mississippi, University, MS 38677, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A {Berry{\textendash}Esseen} bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {701--712},
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     url = {https://www.numdam.org/articles/10.5802/crmath.81/}
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Wu, Songqi; Ma, Xiaohui; Sang, Hailin; Fan, Xiequan. A Berry–Esseen bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales. Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 701-712. doi: 10.5802/crmath.81

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