Geodesic
Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
Serdica Mathematical Journal, Tome 22 (1996) no. 4, pp. 471-496.

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In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum distributions with the help of v-accompanying infinitely divisible distributions are given. The results include, in particular, the description of geometrically infinitely divisible and geometrically stable distributions as well as their domains of attraction.
Keywords: Infinitely Divisible Laws, Geometric Sums, Rate of Convergence, Probability Metrics 
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Klebanov, Lev; Rachev, Svetlozar. Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws. Serdica Mathematical Journal, Tome 22 (1996) no. 4, pp. 471-496. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_4_a0/