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A SIMPLE PROOF OF THE STRONG LAW OF LARGE NUMBERS WITH RATES

Part of: Limit theorems

Published online by Cambridge University Press:  28 March 2018

NUNO LUZIA Open the ORCID record for NUNO LUZIA [Opens in a new window]
NUNO LUZIA*
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-909, Brazil email nuno@im.ufrj.br
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Abstract

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We give a simple proof of the strong law of large numbers with rates, assuming only finite variance. This note also serves as an elementary introduction to the theory of large deviations, assuming only finite variance, even when the random variables are not necessarily independent.

Keywords

strong law of large numbersrates of convergencelarge deviations

MSC classification

Primary: 60F15: Strong theorems
Secondary: 60F10: Large deviations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 513 - 517
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Durrett, R., Probability: Theory and Examples, 2nd edn (Duxbury Press, Belmont, CA, 2004).Google Scholar
Etamadi, N., ‘An elementary proof of the strong law of large numbers’, Z. Wahrscheinlicheitstheorie verw. Geb. 55 (1981), 119–122.Google Scholar
Feller, W., An Introduction to Probability Theory and its Applications, 2nd edn, Vol. 2 (Wiley, New York, 1971).Google Scholar
Fill, J., ‘Convergence rates related to the strong law of large numbers’, Ann. Probab. 11 (1983), 123–142.Google Scholar
Luzia, N., ‘A Borel–Cantelli lemma and its applications’, Trans. Amer. Math. Soc. 366 (2014), 547–560.Google Scholar