Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

Klebanov, Lev, and Rachev, Svetlozar. "Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws." Serdica Mathematical Journal 22.4 (1996): 471-496. <http://eudml.org/doc/11647>.

@article{Klebanov1996,
abstract = {* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.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.},
author = {Klebanov, Lev, Rachev, Svetlozar},
journal = {Serdica Mathematical Journal},
keywords = {Infinitely Divisible Laws; Geometric Sums; Rate of Convergence; Probability Metrics; infinitely divisible laws; geometric sums; rate of convergence; probability metrics},
language = {eng},
number = {4},
pages = {471-496},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws},
url = {http://eudml.org/doc/11647},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Klebanov, Lev
AU - Rachev, Svetlozar
TI - Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 4
SP - 471
EP - 496
AB - * Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.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.
LA - eng
KW - Infinitely Divisible Laws; Geometric Sums; Rate of Convergence; Probability Metrics; infinitely divisible laws; geometric sums; rate of convergence; probability metrics
UR - http://eudml.org/doc/11647
ER -