Geodesic
Unified limit theorems for increments of processes with independent increments
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 601-609

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A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdös–Rényi law, the Shepp law, the Csörgő–Révész law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.
Keywords: increments of processes with independent increments, Erdös–Rényi law, Shepp law, the law of large numbers, the law of the iterated logarithm. 
@article{TVP_2004_49_3_a10,
     author = {A. N. Frolov},
     title = {Unified limit theorems for increments of processes with independent increments},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {601--609},
     publisher = {mathdoc},
     volume = {49},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a10/}
}
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A. N. Frolov. Unified limit theorems for increments of processes with independent increments. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 601-609. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a10/