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arXiv · 1103.3242

Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples

Florence Merlevède·Magda Peligrad
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Abstract

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.

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Florence Merlevède, Magda Peligrad. 2013-03-18. Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples. https://doi.org/10.1214/11-aop694

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