Cramér-type moderate deviations for stationary sequences of bounded random variables

Xiequan Fan

doi:10.1016/j.crma.2019.05.003

Probability theory

Cramér-type moderate deviations for stationary sequences of bounded random variables

Presented by: the Editorial Board

Xiequan Fan ¹

¹ Center for Applied Mathematics, Tianjin University, Tianjin, China

Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 463-477.

Abstract
Résumé

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.

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.

Received: 2018-06-06
Accepted: 2019-05-17
Published online: 2019-05-01

DOI: 10.1016/j.crma.2019.05.003

Author's affiliations:

Xiequan Fan ¹

¹ Center for Applied Mathematics, Tianjin University, Tianjin, China

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     title = {Cram\'er-type moderate deviations for stationary sequences of bounded random variables},
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     pages = {463--477},
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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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