Geometrically strictly semistable laws as the limit laws

Marek Malinowski

ArticleOriginal scientific text

Title

Geometrically strictly semistable laws as the limit laws

Authors ¹

Affiliations

Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra Szafrana 4a, 65-516 Zielona Góra, Poland

Abstract

A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable

X_{p}

such that

X \overset{d}{=} \sum_{k = 1}^{T (p)} X_{p, k}

, where

X_{p, k}

's are i.i.d. copies of

X_{p}

, and random variable T(p) independent of

{X_{p, 1}, X_{p, 2}, ...}

has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.

Keywords

ENG

infinite divisibility, geometric infinite divisibility, geometric semistability, random sums, limit laws, characteristic function

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Title

Geometrically strictly semistable laws as the limit laws

Affiliations

Abstract

Keywords

Bibliography