Laws of large numbers for ratios of uniform random variables

André Adler

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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André Adler. "Laws of large numbers for ratios of uniform random variables." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/275920>.

@article{AndréAdler2015,
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.},
author = {André Adler},
journal = {Open Mathematics},
keywords = {Almost sure convergence; Strong law of large numbers; Weak law of large numbers; Slow variation},
language = {eng},
number = {1},
pages = {null},
title = {Laws of large numbers for ratios of uniform random variables},
url = {http://eudml.org/doc/275920},
volume = {13},
year = {2015},
}

TY - JOUR
AU - André Adler
TI - Laws of large numbers for ratios of uniform random variables
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Almost sure convergence; Strong law of large numbers; Weak law of large numbers; Slow variation
UR - http://eudml.org/doc/275920
ER -

References

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  1. [1] Adler A., Exact strong laws, Bulletin of the Institute of Mathematics Academia Sinica, 2000, 28, 141-166 Zbl0966.60024
  2. [2] Adler A., Rosalsky A., Volodin A., Weak laws with random indices for arrays of random elements in Rademacher type p Banach Spaces, Journal of Theoretical Probability, 1997, 10, 605-623 Zbl0884.60007
  3. [3] Chow Y.S., Teicher H., Probability Theory: Independence, Interchangeability, Martingales, 3rd ed., Springer-Verlag, New York, 1997 
  4. [4] Feller W., An Introduction to Probability Theory and Its Applications, Vol 1., 3rd ed., John Wiley, New York, 1968 
  5. [5] Feller W., An Introduction to Probability Theory and Its Applications, Vol 2., 2nd ed., John Wiley, New York, 1971 
  6. [6] Klass M., Teicher H., Iterated logarithmic laws for asymmetric random variables barely with or without finite mean, Annals Probability, 1977, 5, 861-874 Zbl0372.60042
  7. [7] Rosalsky A., Taylor R.L., Some strong and weak limit theorems for weighted sums of i.i.d. Banach space valued random elements with slowly varying weights. Stochastic Analysis Applications, 2004, 22, 1111-1120 Zbl1158.60305
  8. [8] Seneta E., Regularly Varying Functions, Lecture Notes in Mathematics No. 508, Springer-Verlag, New York, 1976 Zbl0324.26002

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