Lois du logarithme itéré avec pondérations additives-Reference-Cited by-同舟云学术

Lois du logarithme itéré avec pondérations additives

Published:2009-08-03 Issue:12 Volume:137 Page:4255-4257
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Tenenbaum Gérald

Abstract

We provide a very short proof that natural Lindeberg type conditions on the non-negative arithmetic additive function f f ensure the strong law of large numbers and the law of the iterated logarithm for weighted sums ∑ n ⩽ N f ( n ) X n \sum _{n\leqslant N}f(n)X_n for any sequence { X n } n = 1 ∞ \{X_n\}_{n=1}^\infty of i.i.d. random variables.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2009-137-12/S0002-9939-09-10035-7/S0002-9939-09-10035-7.pdf

Reference5 articles.

1. A law of the iterated logarithm for arithmetic functions;Berkes, István;Proc. Amer. Math. Soc.,2007

2. A Skorohod representation and an invariance principle for sums of weighted i.i.d. random variables;Fisher, Evan;Rocky Mountain J. Math.,1992

3. A law of large numbers for arithmetic functions;Fukuyama, Katusi;Proc. Amer. Math. Soc.,2009

4. Convergence of weighted averages of independent random variables;Jamison, Benton;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1965

5. G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, troisième édition, coll. Échelles, Paris, 2008.

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