G-casual Stable Probability Distributions

TL;DR

This paper introduces a generalized concept of stable probability distributions called G-casual stability, providing an algebraic framework for discrete stable distributions on integers and presenting related limit theorems.

Contribution

It proposes the notion of G-casual stability, offering a new algebraic approach to discrete stable distributions on integers, differing from traditional limit definitions.

Findings

G-casual stability generalizes stable distributions.

Provides algebraic characterizations for discrete stable distributions.

Includes examples of limit theorems for these distributions.

Abstract

A generalization of stable and casual stable probability distribution is proposed. The notion of $\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\mathbb Z$ of integers. In contrary to limit definition of stable distributions on $\mathbb Z$ our has algebraic character. Examples of corresponding limit theorems are given. Keywords: stable distributions; casual stable distribution; discrete stable distributions; limit theorems