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Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables
Authors:Sergey Utev  Magda Peligrad
Institution:(1) School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom;(2) Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, 45221-0025
Abstract:The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences.
Keywords:Maximal inequalities  invariance principles  dependent random variables  Rosenthal inequality
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