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Zbl 0928.60025
Peligrad, Magda; Gut, Allan
Almost-sure results for a class of dependent random variables. (English)
[J] J. Theor. Probab. 12, No.1, 87-104 (1999). ISSN 0894-9840; ISSN 1572-9230/e

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.''\par 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).
[B.Le Gac (Marseille)]

MSC 2000:: *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

Cited in: Zbl 1193.60045 Zbl 1201.60048

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Zentralblatt MATH Berlin [Germany]