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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1

Issues

Volume 13 (2015)

Laws of large numbers for ratios of uniform random variables

André Adler
Published Online: 2015-09-25 | DOI: https://doi.org/10.1515/math-2015-0054

Abstract

Let {Xnn n ≥ 1} and {Yn, n ≥ 1} be two sequences of uniform random variables. We obtain various strong and weak laws of large numbers for the ratio of these two sequences. Even though these are uniform and naturally bounded random variables the ratios are not bounded and have an unusual behaviour creating Exact Strong Laws.

Keywords: Almost sure convergence; Strong law of large numbers; Weak law of large numbers; Slow variation

References

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About the article

Received: 2015-05-25

Accepted: 2015-09-03

Published Online: 2015-09-25


Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0054.

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© 2015. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[2]
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[3]
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[4]
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