Geodesic
Limit theorems for
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 259-283 Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive universal strong limit theorems for increments of compound renewal processes which unifies the strong law of large numbers, the Erdős–Rényi law, the Csörgő-Révész law and the law of the iterated logarithm for such processes. New results are obtained under various moment assumptions on distributions of random variables generating the process. In particular, it is investigated the case of distributions from domains of attraction of a normal law and completely asymmetric stable laws with index $\alpha\in(1,2)$. 
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A. N. Frolov. Limit theorems for. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 259-283. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a15/

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