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March 2013 Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples
Florence Merlevède, Magda Peligrad
Ann. Probab. 41(2): 914-960 (March 2013). DOI: 10.1214/11-AOP694

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. "Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples." Ann. Probab. 41 (2) 914 - 960, March 2013. https://doi.org/10.1214/11-AOP694

Information

Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1274.60056
MathSciNet: MR3077530
Digital Object Identifier: 10.1214/11-AOP694

Subjects:
Primary: 60E15 , 60G10 , 60G48

Keywords: martingale , maximal inequality , moment inequality , projective conditions , Rosenthal inequality , Stationary sequences

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • March 2013
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