Geodesic
On asymptotic behaviour of increments of sums over increasing runs
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 248-260

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We investigate the almost sure asymptotic behaviour of increments of sums of i.i.d. random variables over increasing runs in associate sequence. The Shepp law, the Erdős–Rényi law and the Csörgő–Révész laws are obtained for increments of sums over increasing runs formed by random variables which take its values in a fixed interval. 
@article{ZNSL_2001_278_a14,
     author = {A. N. Frolov},
     title = {On asymptotic behaviour of increments of sums over increasing runs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {248--260},
     publisher = {mathdoc},
     volume = {278},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a14/}
}
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A. N. Frolov. On asymptotic behaviour of increments of sums over increasing runs. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 248-260. http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a14/