Illustration par quelques exemples des lois strictement stables dans un c\^one convexe

TL;DR

This paper explores the generalization of stability of random variables within convex cones, presenting examples of stable distributions and their relation to Poisson processes, extending classical results to this geometric setting.

Contribution

It introduces new examples of strictly stable and max-stable distributions in convex cones, highlighting differences from classical Banach space results and linking Poisson processes to these distributions.

Findings

Examples of strictly stable distributions in convex cones

Relationship between Poisson processes and stable distributions

Extension of stability concepts beyond Banach spaces

Abstract

The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach spaces. Some examples of strictly stable distributions and max-stable distributions are presented in this paper in order to exhibit the relationship between the Poisson process and the stable distributions on convex cones.