Comptes Rendus
no. 21-22
Probability theory/Statistics
Sharp large deviations under Bernsteinʼs condition
[Grandes déviations précises sous la condition de Bernstein]

Présenté par : Michel Talagrand

Xiequan Fan1, 2 ; Ion Grama1 ; Quansheng Liu1
1 Université de Bretagne-Sud, UMR 6205, LMBA, 56000 Vannes, France
2 Regularity Team, Inria and MAS Laboratory, École centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 845-848.

Nous améliorons lʼinégalité de Bernstein pour les sommes de variables aléatoires non bornées. En particulier, nous établissons un développement de grandes déviations précises de type Cramér et Bahadur–Rao.

We improve Bernsteinʼs inequality for sums of non-bounded random variables. In particular, we establish a sharp large deviation expansion similar to that of Cramér and Bahadur–Rao.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.015
Xiequan Fan 1, 2 ; Ion Grama 1 ; Quansheng Liu 1

1 Université de Bretagne-Sud, UMR 6205, LMBA, 56000 Vannes, France
2 Regularity Team, Inria and MAS Laboratory, École centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France 
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Xiequan Fan; Ion Grama; Quansheng Liu. Sharp large deviations under Bernsteinʼs condition. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 845-848. doi : 10.1016/j.crma.2013.10.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.015/

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