Subordinators on Feller Topological Monoids

TL;DR

This paper extends the classical theory of subordinators to a new class of topological monoids called Feller topological monoids, providing generalized Lévy-Khintchine and Lévy-Itô formulas.

Contribution

It introduces Feller topological monoids and develops a generalized theory of subordinators with Lévy-Khintchine and Lévy-Itô representations.

Findings

Established a Lévy-Khintchine type formula for subordinators on Feller topological monoids.

Derived a Lévy-Itô like decomposition in this generalized setting.

Generalized classical subordinators to a broader algebraic and topological context.

Abstract

We investigate a class of topological monoids with a suitable family of characters which we call Feller topological monoids. We extend the classical notion of subordinators to subordinators on Feller topological monoids. Under suitable assumptions, we prove a L\'evy-Khintchine type representation for such subordinators. In addition, a L\'evy-It\^o like decomposition is obtained. These formulae generalize the classical ones for subordinators.