Subordinators on Feller Topological Monoids

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.