A Bernstein type inequality and moderate deviations for weakly dependent sequences
Merlevède, Florence ; Peligrad, Magda ; Rio, Emmanuel
HAL, inria-00358525 / Harvested from HAL
Text on HAL
In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviations results. Applications include classes of Markov chains, functions of linear processes with absolutely regular innovations and ARCH models
Publié le : 2009-02-03
Classification:  Deviation inequality,  moderate deviations principle,  semiexponential tails,  weakly dependent sequences,  strong mixing,  absolute regularity,  linear processes,  Mathematical subject classification (2000): 60E15, 60F10,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{inria-00358525,
     author = {Merlev\`ede, Florence and Peligrad, Magda and Rio, Emmanuel},
     title = {A Bernstein type inequality and moderate deviations for weakly dependent sequences},
     journal = {HAL},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00358525}
}

Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel. A Bernstein type inequality and moderate deviations for weakly dependent sequences. HAL, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/inria-00358525/