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

Abstract : The aim of this paper is to propose new Rosenthal-type inequalities for moments of order p larger 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. (2007) and Rio (2009), 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's maximal inequality for martingales and dyadic induction. Various applications are also provided.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00795399
Contributor : Florence Merlevède <>
Submitted on : Thursday, February 28, 2013 - 9:46:44 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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  • HAL Id : hal-00795399, version 1

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Florence Merlevède, Magda Peligrad. Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples. Annals of Probability, Institute of Mathematical Statistics, 2013, ? (?). ⟨hal-00795399⟩

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