Geodesic
On asymptotic behaviour of increments of random fields
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 191-207

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We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices where an exponential moment does not exist. Our theorems yield the strong law of large numbers, the law of the iterated logarithm and the Csörgő-Révész laws for random fields. New results are obtained for distributions from domains of attraction of a normal law and completely asymmetric stable laws with index $\alpha\in(1,2)$. 
@article{ZNSL_2003_298_a12,
     author = {A. N. Frolov},
     title = {On asymptotic behaviour of increments of random fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {191--207},
     publisher = {mathdoc},
     volume = {298},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a12/}
}
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A. N. Frolov. On asymptotic behaviour of increments of random fields. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 191-207. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a12/