Peligrad, Magda; Gut, Allan Almost-sure results for a class of dependent random variables. (English) Zbl 0928.60025 J. Theor. Probab. 12, No. 1, 87-104 (1999). 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). Reviewer: B.Le Gac (Marseille) Cited in 4 ReviewsCited in 85 Documents MSC: 60F15 Strong limit theorems 60G60 Random fields Keywords:Marcinkiewicz-Zygmund type results; maximal coefficient of correlation; random fields Citations:Zbl 0448.60024; Zbl 0438.60027 PDFBibTeX XMLCite \textit{M. Peligrad} and \textit{A. Gut}, J. Theor. Probab. 12, No. 1, 87--104 (1999; Zbl 0928.60025) Full Text: DOI