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Zbl 1012.60022
Utev, Sergey; Peligrad, Magda
Maximal inequalities and an invariance principle for a class of weakly dependent random variables. (English)
[J] J. Theor. Probab. 16, No.1, 101-115 (2003). ISSN 0894-9840; ISSN 1572-9230/e

Summary: 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.

MSC 2000:: *60E15 Inequalities in probability theory

Keywords: maximal inequalities; invariance principles; dependent random variables; Rosenthal inequality

Cited in: Zbl 1122.60032 Zbl 1110.60020 Zbl 1087.60003

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