PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Banach Center Publications

2010 | 90 | 1 | 39-65
Tytuł artykułu

### Geometric infinite divisibility, stability, and self-similarity: an overview

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of $N_p$ components for each p ∈ (0,1), where $N_p$ is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable. This leads to broad classes of probability distributions closely connected with their classical counterparts. We review fundamental properties of these distributions and discuss further extensions connected with geometric sums, including multivariate and operator geometric stability, discrete analogs, and geometric self-similarity.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
39-65
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
• Department of Mathematics & Statistics, University of Nevada, Reno, NV 89523, USA
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory