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Maximum of partial sums and an invariance principle for a class of weak dependent random variables. (English) Zbl 0899.60044

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 and the convergence of the moments in the central limit theorem.

MSC:

60G70 Extreme value theory; extremal stochastic processes
60G10 Stationary stochastic processes
60F15 Strong limit theorems
60E15 Inequalities; stochastic orderings
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