Almost-sure results for a class of dependent random variables. (English) Zbl 0928.60025

Authors’ abstract: “The main of this note is to establish almost sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by \(\mathbb{Z}^d_+\) – the positive \(d\)-dimensional lattice points – and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.”
The authors get in particular a strong law of large numbers similar to N. Etemadi’s one [Z. Wahrscheinlichkeitstheorie Verw. Geb. 55, 119-122 (1981; Zbl 0438.60027)], but under a weaker condition: they assume only that the maximal coefficient of correlation is \(<1\), instead of pairwise independence in Etemadi’s theorem. A corresponding statement is also given for \(d\)-dimensional random fields (Theorem 6).


60F15 Strong limit theorems
60G60 Random fields
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