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.
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(Received 31 January 2000; in revised form 5 April 2000)
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Scheffler, HP., Becker-Kern, P. A Law of the Iterated Logarithm for Randomly Stopped Sums of Heavy Tailed Random Vectors. Mh Math 130, 329–347 (2000). https://doi.org/10.1007/s006050070031
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DOI: https://doi.org/10.1007/s006050070031