G-casual Stable Probability 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