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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 17, Fasc. 1,
pages 65 - 77
 

LARGE DEVIATIONS AND LAW OF THE ITERATED LOGARITHM FOR GENERALIZED DOMAINS OF ATTRACTION

Hans-Peter Scheffler

Abstract: Suppose X,X ,X ,... 1 2 are i.i.d. random vectors, S = sum n X n i=1 i and A n are linear operators such that A S n n converges in law to some full random vector Y. Then we say that X belongs to the strict generalized domain of attraction of Y. We show that if Y has no normal component, then (A S ) n n satisfies a large deviation principle. This large deviation result is used to show that a law of the iterated logarithm for (A S ) n n holds, which gives the precise growth behavior of the sample paths of the random walk (S ). n

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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