Comptes Rendus
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]
Songqi Wu1 ; Xiaohui Ma1 ; Hailin Sang2 ; Xiequan Fan1 
1 Center for Applied Mathematics, Tianjin University, Tianjin, China
2 Department of Mathematics, The University of Mississippi, University, MS 38677, USA
Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 701-712.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.5802/crmath.81
Songqi Wu 1 ; Xiaohui Ma 1 ; Hailin Sang 2 ; Xiequan Fan 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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     author = {Songqi Wu and Xiaohui Ma and Hailin Sang and Xiequan Fan},
     title = {A {Berry{\textendash}Esseen} bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {701--712},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2020},
     doi = {10.5802/crmath.81},
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Songqi Wu; Xiaohui Ma; Hailin Sang; Xiequan Fan. A Berry–Esseen bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 701-712. doi : 10.5802/crmath.81. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.81/

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