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Title: Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
Authors: Klebanov, Lev
Rachev, Svetlozar
Keywords: Infinitely Divisible Laws
Geometric Sums
Rate of Convergence
Probability Metrics
Issue Date: 1996
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 22, No 4, (1996), 471p-496p
Abstract: 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.
Description: * Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.
ISSN: 1310-6600
Appears in Collections:Volume 22 Number 4

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