Strong limit theorems for blockwise -dependent and blockwise quasi-orthogonal sequences of random variables

Author:
F. Móricz

Journal:
Proc. Amer. Math. Soc. **101** (1987), 709-715

MSC:
Primary 60F15; Secondary 60G50

MathSciNet review:
911038

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Abstract: Let be a sequence of random variables with zero mean and finite variance . We say that is blockwise -dependent if for each large enough the following is true: if we remove or more consecutive 's from the dyadic block , then the two remaining portions are independent. We say that is blockwise quasiorthogonal if for each , the expectations are small in a certain sense again within the dyadic block . Blockwise independence and blockwise orthogonality are particular cases of the above notions, respectively.

We study the a.s. behavior of the series and that of the first arithmetic means . It turns out that the classical strong limit theorems, with one exception, remain valid in this more general setting, too.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911038-3

Keywords:
-dependent random variables,
orthogonal random variables,
first arithmetic means,
strong limit theorems,
strong laws of large numbers

Article copyright:
© Copyright 1987
American Mathematical Society