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

Présenté par : Michel Talagrand

Fan, Xiequan1, 2 ; Grama, Ion1 ; Liu, Quansheng1
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, Tome 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
Fan, Xiequan 1, 2 ; Grama, Ion 1 ; Liu, Quansheng 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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Fan, Xiequan; Grama, Ion; Liu, Quansheng. Sharp large deviations under Bernsteinʼs condition. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 845-848. doi : 10.1016/j.crma.2013.10.015. http://www.numdam.org/articles/10.1016/j.crma.2013.10.015/

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