Comptes Rendus
no. 5
Probability theory
Cramér-type moderate deviations for stationary sequences of bounded random variables
[Déviations modérées de type Cramér pour les suites stationnaires]

Présenté par : the Editorial Board

Xiequan Fan1
1 Center for Applied Mathematics, Tianjin University, Tianjin, China
Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 463-477.

Nous dérivons les déviations modérées de type Cramér pour des suites stationnaires de variables aléatoires bornées. Nos résultats impliquent les principes de déviation modérée et un théorème de Berry–Esseen. Nous discutons les applications aux inégalités de couplage quantile et aux fonctions de suites mélangeantes et de chaînes de Markov contractantes.

We derive Cramér-type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry–Esseen bound. Applications to quantile coupling inequalities, functions of ϕ-mixing sequences, and contracting Markov chains are discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.05.003
Xiequan Fan 1

1 Center for Applied Mathematics, Tianjin University, Tianjin, China 
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Xiequan Fan. Cramér-type moderate deviations for stationary sequences of bounded random variables. Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 463-477. doi : 10.1016/j.crma.2019.05.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.05.003/

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