A generalized Law of the Iterated Logarithm for the largest observation of a triangular array

• Autorzy: Adler A.
• Języki publikacji: EN

Abstrakty

EN

Consider independent and identically distributed random variables {X, X_kj1≤j≤k, k≥1} from a particular distribution with EX=∞.Weshow that there exists an unusual generalized Law of the Iterated Logarithm involving max _1≤j≤kX_kj.

Słowa kluczowe

EN

Almost sure convergence; weak law of large numbers; law of the iterated logarithm

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 1
• Strony: 149--157
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Adler A.

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

Bibliografia

• [1] A. Adler, Generalized one-sided laws of the iterated logarithm for random variables barely with or without finite mean, J. Theoret. Probab. 3 (1990), pp. 587-598.
• [2] A. Adler, An unusual strong law of large numbers for the largest observation in a triangular array, Bull. Inst. Math. Acad. Sinica 29 (2001), to appear.
• [3] Y. S. Chow and H. Teicher, Probability Theory. Independence, Interchangeability, Martingales, 2nd edition, Springer, New York 1988.
• [4] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 4th edition, Academic Press, New York 1980.
• [5] M. Klass and H. Teicher, Iterated logarithm laws for asymmetric random variables barely with or without finite mean, Ann. Probab. 5 (1977), pp. 861-874.