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Laws of the iterated logarithm in the tails for weighted uniform empirical processes

J.H.J. Einmahl, David M. Mason

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Abstract

Characterizations of laws of the iterated logarithm for the supremum of weighted uniform $\lbrack 0, 1\rbrack^d$ empirical processes taken over increasingly smaller regions near the origin are obtained. These results have proven to be a valuable tool in the derivation of laws of the iterated logarithm for sums of extreme values. They also constitute a further continuation of the study of the almost sure behavior of weighted uniform empirical processes, which in a certain sense was begun by Csaki.

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Characterizations of laws of the iterated logarithm for the supremum of weighted uniform $\lbrack 0, 1\rbrack^d$ empirical processes taken over increasingly smaller regions near the origin are obtained. These results have proven to be a valuable tool in the derivation of laws of the iterated logarithm for sums of extreme values. They also constitute a further continuation of the study of the almost sure behavior of weighted uniform empirical processes, which in a certain sense was begun by Csaki.

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Available abstract

Characterizations of laws of the iterated logarithm for the supremum of weighted uniform $\lbrack 0, 1\rbrack^d$ empirical processes taken over increasingly smaller regions near the origin are obtained. These results have proven to be a valuable tool in the derivation of laws of the iterated logarithm for sums of extreme values. They also constitute a further continuation of the study of the almost sure behavior of weighted uniform empirical processes, which in a certain sense was begun by Csaki.

Key concepts: Iterated logarithm, Law of the iterated logarithm, Infimum and supremum, Logarithm, Mathematics, Iterated function, Applied mathematics, Discrete mathematics

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