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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] B. A. Sevastyanov, “Predelnyi zakon Puassona v skheme summ zavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., XVII:4 (1972), 733–738

[2] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, izd-vo «Nauka», Moskva, 1972

[3] A. M. Zubkov, V. G. Mikhailov, “Predelnye raspredeleniya sluchainykh velichin, svyazannykh s dlinnymi povtoreniyami v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatn. i ee primen., XIX:1 (1974), 173–181 | MR

[4] V. G. Mikhailov, “Predelnye raspredeleniya sluchainykh velichin, svyazannykh s mnogokratnymi dlinnymi povtoreniyami v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatn. i ee primen., XIX:1 (1974), 182–187