Lois du logarithme itéré avec pondérations additives
HTML articles powered by AMS MathViewer
- by Gérald Tenenbaum
- Proc. Amer. Math. Soc. 137 (2009), 4255-4257
- DOI: https://doi.org/10.1090/S0002-9939-09-10035-7
- Published electronically: August 3, 2009
- PDF | Request permission
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.References
- István Berkes and Michel Weber, A law of the iterated logarithm for arithmetic functions, Proc. Amer. Math. Soc. 135 (2007), no. 4, 1223–1232. MR 2262929, DOI 10.1090/S0002-9939-06-08557-1
- Evan Fisher, A Skorohod representation and an invariance principle for sums of weighted i.i.d. random variables, Rocky Mountain J. Math. 22 (1992), no. 1, 169–179. MR 1159950, DOI 10.1216/rmjm/1181072802
- Katusi Fukuyama and Yutaka Komatsu, A law of large numbers for arithmetic functions, Proc. Amer. Math. Soc. 137 (2009), no. 1, 349–352. MR 2439459, DOI 10.1090/S0002-9939-08-09517-8
- Benton Jamison, Steven Orey, and William Pruitt, Convergence of weighted averages of independent random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 4 (1965), 40–44. MR 182044, DOI 10.1007/BF00535481
- G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, troisième édition, coll. Échelles, Paris, 2008.
Bibliographic Information
- Gérald Tenenbaum
- Affiliation: Institut Élie Cartan, Université Henri Poincaré–Nancy 1, BP 239, 54506 Vandœuvre lèes Nancy Cedex, France
- ORCID: 0000-0002-0478-3693
- Email: gerald.tenenbaum@iecn.u-nancy.fr
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4255-4257
- MSC (2000): Primary 60F15, 11N37; Secondary 60G50
- DOI: https://doi.org/10.1090/S0002-9939-09-10035-7
- MathSciNet review: 2538586