Abstract.
For a random vector belonging to the (generalized) domain of operator semistable attraction of some nonnormal law we prove various variants of Chover's law of the iterated logarithm for the partial sum. Furthermore we also derive some large deviation results necessary for the proof of our main theorems.
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Received: 30 September 1998 / Revised version: 28 May 1999
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Scheffler, HP. A law of the iterated logarithm for heavy-tailed random vectors. Probab Theory Relat Fields 116, 257–271 (2000). https://doi.org/10.1007/PL00008729
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DOI: https://doi.org/10.1007/PL00008729
- Mathematics Subject Classification (1991): 60F15, 60F10, 60E07
- Key words and phrases: Regularly varying measures – Generalized domains of semistable attraction – Operator semistable laws – Large deviations – Law of the iterated logarithm