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).

MSC:

 60F15 Strong limit theorems 60G60 Random fields

Citations:

Zbl 0448.60024; Zbl 0438.60027
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