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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lois du logarithme itéré avec pondérations additives


Author: Gérald Tenenbaum
Journal: Proc. Amer. Math. Soc. 137 (2009), 4255-4257
MSC (2000): Primary 60F15, 11N37; Secondary 60G50
Published electronically: August 3, 2009
MathSciNet review: 2538586
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Abstract: We provide a very short proof that natural Lindeberg type conditions on the non-negative arithmetic additive function $ f$ ensure the strong law of large numbers and the law of the iterated logarithm for weighted sums $ \sum_{n\leqslant N}f(n)X_n$ for any sequence $ \{X_n\}_{n=1}^\infty$ of i.i.d. random variables.


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Additional Information

Gérald Tenenbaum
Affiliation: Institut Élie Cartan, Université Henri Poincaré–Nancy 1, BP 239, 54506 Vandœuvre lèes Nancy Cedex, France
Email: gerald.tenenbaum@iecn.u-nancy.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10035-7
PII: S 0002-9939(09)10035-7
Received by editor(s): April 25, 2009
Received by editor(s) in revised form: April 29, 2009
Published electronically: August 3, 2009
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.