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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 24, Fasc. 2,
pages 281 - 295
 

LIMITING BEHAVIOR OF WEIGHTED SUMS OF HEAVY-TAILED RANDOM VECTORS AND APPLICATIONS

Chen Pingyan
Hans-Peter Scheffler

Abstract: We present an integral test to determine the limiting behavior of weighted sums of i.i.d. Rd -valued random vectors belonging to the (generalized) domain of operator semistable attraction of some nonnormal law, and deduce a version of Chover’s law of the iterated logarithm for them. As applications, the corresponding limit results for some classical summability methods are also established.

2000 AMS Mathematics Subject Classification: 60F15, 60F10, 60E07.

Key words and phrases: Generalized domains of semistable attraction, operator semistable laws, laws of the iterated logarithm, integral test.

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