On exact strong laws for sums of multidimensionally indexed random variables

• Autorzy: Adler A. , Qi Y.
• Języki publikacji: EN

Abstrakty

EN

Let {X, X_n, n ∈ Z^d₊} be independent and identically distributed random variables satisfying xP (|X| > x) ≈ L(x) with either EX = 0 or E|X| = ∞, where L(x) is slowly varying at infinity. This paper proves that there always exist sequencesof constants {a_n} and {B_N} such that an Exact Strong Law holds, that is [wzór] a_n X_n/B_N → 1 almost surely as N → ∞.

Słowa kluczowe

EN

strong law of large numbers; almost sure convergence; exact strong laws; multidimensionally indexed random variables

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 2
• Strony: 305--313
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Adler A.

• Department of Mathematics, Illinois Institute of Technology, Chicago, IL 60616, U.S.A.

autor

Qi Y.

• Department of Mathematics and Statistics, University of Minnesota Duluth, CCTR 140, 1117 University Drive Duluth, MN 55812, U.S.A.

Bibliografia

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• [4] A. Adler, Exact strong laws, Bull. Inst. Math. Acad Sinica 28 (2000), pp. 141-166.
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• [6] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University, New York 1987.
• [7] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 3rd edition, Springer, New York 1997.
• [8] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edition, Wiley, New York 1971.