Integral analogues of almost sure limit theorems |
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Authors: | Alexey Chuprunov István Fazekas |
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Institution: | (1) Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya 17, 420008 Kazan, Russia;(2) Faculty of Informatics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary |
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Abstract: | Summary An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable processes, moreover for processes being in the domain of attraction of a stable law or being in the domain of geometric partial attraction of a semistable or a max-semistable law. |
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Keywords: | regularly varying function almost sure limit theorem process with independent stationary increments infinitely divisible law stable law semistable law max-semistable law domain of attraction |
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