Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
Merlevède, Florence ; Peligrad, Magda
arXiv, 1103.3242 / Harvested from arXiv
Text on arXiv
The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob maximal inequality for martingales and dyadic induction. Various applications are also provided.
Publié le : 2011-03-16
Classification:  Mathematics - Probability 
@article{1103.3242,
     author = {Merlev\`ede, Florence and Peligrad, Magda},
     title = {Rosenthal-type inequalities for the maximum of partial sums of
  stationary processes and examples},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1103.3242}
}

Merlevède, Florence; Peligrad, Magda. Rosenthal-type inequalities for the maximum of partial sums of
  stationary processes and examples. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1103.3242/