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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 21, Fasc. 1,
pages 149 - 157
 

A GENERALIZED LAW OF THE ITERATED LOGARITHM FOR THE LARGEST OBSERVATION OF A TRIANGULAR ARRAY

André Adler

Abstract: Consider independent and identically distributed random variables (X, X ,1 < j < k,k > 1) kj from a particular distribution with EX = oo . We show that there exists an unusual generalized Law of the Iterated Logarithm involving max X . 1<j<k kj

1991 AMS Mathematics Subject Classification: 60F05, 60F15.

Key words and phrases: Almost sure convergence, weak law of large numbers, law of the iterated logarithm.

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