A Law of the Iterated Logarithm for Randomly Stopped Sums of Heavy Tailed Random Vectors |
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Authors: | Hans-Peter Scheffler Peter Becker-Kern |
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Institution: | (1) University of Dortmund, Germany, DE |
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Abstract: | Let be an i.i.d. sequence of -valued random vectors belonging to the generalized domain of semistable attraction of some nonnormal law. Assume further
that is a sequence of positive integer valued random variables such that for some
for some discrete positive random variable D, where we do not assume that and are independent. Let . Then various laws of the iterated logarithm for the norm of as well as the radial projection onto a unit vector θ are presented.
(Received 31 January 2000; in revised form 5 April 2000) |
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Keywords: | 2000 Mathematics Subject Classification: 60F15 60E07 60F05 |
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