Maximal inequalities and an invariance principle for a class of weakly dependent random variables. (English) Zbl 1012.60022

Utev, Sergey; Peligrad, Magda

J. Theor. Probab. 16, No. 1, 101-115 (2003).

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:

60E15

Inequalities; stochastic orderings

Keywords:

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