Laws of large numbers for ratios of uniform random variables
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 cr...
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De Gruyter
2015-09-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2015-0054 |
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doaj-34f0a257d57c478facf436523abf93612021-09-06T19:20:07ZengDe GruyterOpen Mathematics2391-54552015-09-0113110.1515/math-2015-0054math-2015-0054Laws of large numbers for ratios of uniform random variablesAdler André0Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, 60616, USALet {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.https://doi.org/10.1515/math-2015-0054almost sure convergencestrong law of large numbersweak law of large numbersslow variation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Adler André |
| spellingShingle |
Adler André Laws of large numbers for ratios of uniform random variables Open Mathematics almost sure convergence strong law of large numbers weak law of large numbers slow variation |
| author_facet |
Adler André |
| author_sort |
Adler André |
| title |
Laws of large numbers for ratios of uniform random variables |
| title_short |
Laws of large numbers for ratios of uniform random variables |
| title_full |
Laws of large numbers for ratios of uniform random variables |
| title_fullStr |
Laws of large numbers for ratios of uniform random variables |
| title_full_unstemmed |
Laws of large numbers for ratios of uniform random variables |
| title_sort |
laws of large numbers for ratios of uniform random variables |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2015-09-01 |
| description |
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. |
| topic |
almost sure convergence strong law of large numbers weak law of large numbers slow variation |
| url |
https://doi.org/10.1515/math-2015-0054 |
| work_keys_str_mv |
AT adlerandre lawsoflargenumbersforratiosofuniformrandomvariables |
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1717777264485072896 |