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.