Strong limit theorems for blockwise dependent and blockwise quasiorthogonal sequences of random variables
Author:
F. Móricz
Journal:
Proc. Amer. Math. Soc. 101 (1987), 709715
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:
http://dx.doi.org/10.1090/S00029939198709110383
PII:
S 00029939(1987)09110383
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
