Laws of large numbers for ratios of uniform random variables

• Autorzy: André Adler
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-05-25

zaakceptowano

2015-09-03

online

2015-09-25

Twórcy

autor

André Adler

• Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, 60616, USA

Bibliografia

• [1] Adler A., Exact strong laws, Bulletin of the Institute of Mathematics Academia Sinica, 2000, 28, 141-166
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• [3] Chow Y.S., Teicher H., Probability Theory: Independence, Interchangeability, Martingales, 3rd ed., Springer-Verlag, New York, 1997
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• [5] Feller W., An Introduction to Probability Theory and Its Applications, Vol 2., 2nd ed., John Wiley, New York, 1971
• [6] Klass M., Teicher H., Iterated logarithmic laws for asymmetric random variables barely with or without finite mean, Annals Probability, 1977, 5, 861-874
• [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
• [8] Seneta E., Regularly Varying Functions, Lecture Notes in Mathematics No. 508, Springer-Verlag, New York, 1976

Identyfikatory

DOI

10.1515/math-2015-0054