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

Klebanov, Lev; Rachev, Svetlozar

Serdica Mathematical Journal (1996)

- Volume: 22, Issue: 4, page 471-496
- ISSN: 1310-6600

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topKlebanov, 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 -

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