A maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications

Peligrad, Magda; Utev, Sergey; Wu, Wei

doi:10.1090/S0002-9939-06-08488-7

A maximal $\mathbb {L}_{p}$-inequality for stationary sequences and its applications
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by Magda Peligrad, Sergey Utev and Wei Biao Wu

Proc. Amer. Math. Soc. 135 (2007), 541-550

DOI: https://doi.org/10.1090/S0002-9939-06-08488-7

Published electronically: August 8, 2006

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Abstract:

The paper aims to establish a new sharp Burkholder-type maximal inequality in $\mathbb {L}_p$ for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of certain maps of Bernoulli shifts processes.

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