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Open Mathematics

formerly Central European Journal of Mathematics

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

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Volume 13, Issue 1


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


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


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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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