Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2025-01-01T16:52:02.937Z Has data issue: false hasContentIssue false
  • English
  • Français

A Central Limit Theorem for Multiplicative Systems

Published online by Cambridge University Press:  20 November 2018

J. Komlós
J. Komlós*
Affiliation:
Hungarian Academy of Sciences, Budapest Hungary McGill University, Montreal, Quebec
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The central limit theorem was originally proved for independent random variables. The independence is a very strong notion and hard to check. There are various efforts to prove different theorems on independent variables (e.g. strong law of large numbers, central limit theorem, the law of iterated logarithm, convergence theorem of Kolmogorov) under weaker conditions, like mixing, martingale-difference, orthogonality. Among these concepts the weakest one is orthogonality, but this ensures only the validity of law of large numbers.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 67 - 73
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Alexits, G., Convergence problems of orthogogal series, Akad. Kiadό, Budapest, 1961.Google Scholar
2. Doob, F.L., Stochastic processes, Wiley, New York.Google Scholar
3. Alexits, G. and Sharma, A., The influence of Lebesgue functions on the convergence and summability of function series, Acta Math. Acad. Sci. Hungar. (to appear).Google Scholar
4. Révész, P., Some remarks on strongly multiplicative systems, Acta Math. Acad. Sci. Hungar. 16 (1965), p. 441.Google Scholar
5. Gaposkin, V.F., General limit theorem for strongly multiplicative systems (Russian) Sibirsk Mat. Z., 6 (1969).Google Scholar
6. Takahashi, S., Notes on the law of iterated logarithm, Studia Sci. Math. Hungar (to appear).Google Scholar
7. Révész, P., Note to a paper of S. Takahashi, Studia Sci. Math. Hungar (to appear).Google Scholar