The Annals of Probability

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

Florence Merlevède and Magda Peligrad

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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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Ann. Probab., Volume 41, Number 2 (2013), 914-960.

First available in Project Euclid: 8 March 2013

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 60G10: Stationary processes 60G48: Generalizations of martingales

Moment inequality maximal inequality Rosenthal inequality stationary sequences martingale projective conditions


Merlevède, Florence; Peligrad, Magda. Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples. Ann. Probab. 41 (2013), no. 2, 914--960. doi:10.1214/11-AOP694.

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