Geodesic
Convergence to a~process with independent increments in a~scheme of increasing sums of dependent random variables
Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 271-286

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This article derives conditions under which a sequence of random set functions on subsets of a finite-dimensional space constructed in terms of increasing sums of dependent nonnegative random variables converges (in the sense of convergence of finite-dimensional distributions) to a random set function with independent increments which have infinitely divisible distributions. The results obtained are applied to the problem of the number of long repetitions in a sequence of trials. Bibliography: 4 titles. 
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     author = {V. G. Mikhailov},
     title = {Convergence to a~process with independent increments in a~scheme of increasing sums of dependent random variables},
     journal = {Sbornik. Mathematics},
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     year = {1974},
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     url = {http://geodesic.mathdoc.fr/item/SM_1974_23_2_a6/}
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V. G. Mikhailov. Convergence to a~process with independent increments in a~scheme of increasing sums of dependent random variables. Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 271-286. http://geodesic.mathdoc.fr/item/SM_1974_23_2_a6/