Moderate deviations for stationary sequences of bounded random variables
Dedecker, Jérôme ; Merlevède, Florence ; Peligrad, Magda ; Utev, Sergey
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009), p. 453-476 / Harvested from Numdam
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Dans cet article, nous établissons un principe de déviation modérée pour des suites stationnaires de variables aléatoires bornées sous différentes conditions projectives. Nous appliquons ces résultats aux suites ϕ-mélangeantes, à certaines chaînes de Markov contractantes, aux transformations uniformément dilatantes de l'intervalle, ainsi qu'à la marche aléatoire symétrique sur le cercle.

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of ϕ-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.

Publié le : 2009-01-01
DOI : https://doi.org/10.1214/08-AIHP169
Classification:  60F10,  60G10 
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     author = {Dedecker, J\'er\^ome and Merlev\`ede, Florence and Peligrad, Magda and Utev, Sergey},
     title = {Moderate deviations for stationary sequences of bounded random variables},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {45},
     year = {2009},
     pages = {453-476},
     doi = {10.1214/08-AIHP169},
     mrnumber = {2521409},
     zbl = {1172.60005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2009__45_2_453_0}
}

Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda; Utev, Sergey. Moderate deviations for stationary sequences of bounded random variables. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) pp. 453-476. doi : 10.1214/08-AIHP169. http://gdmltest.u-ga.fr/item/AIHPB_2009__45_2_453_0/

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