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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 $\bbfZ^d_+$ -- 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 {\it 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).

60F15Strong limit theorems
60G60Random fields
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