Uniformly continuous semigroups of sublinear transition operators

TL;DR

This paper studies uniformly continuous semigroups of sublinear transition operators on Banach spaces, showing they are generated by exponentials of bounded sublinear rate operators, thus characterizing their structure.

Contribution

It establishes that all such semigroups are exponential families generated by bounded sublinear operators, providing a complete characterization.

Findings

Semigroups are generated by exponentials of sublinear rate operators.

Any uniformly continuous semigroup of sublinear transition operators has this exponential form.

The structure of these semigroups is fully characterized by bounded sublinear operators.

Abstract

In this work I investigate uniformly continuous semigroups of sublinear transition operators on the Banach space of bounded real-valued functions on some countable set. I show how the family of exponentials of a bounded sublinear rate operator is such a semigroup, and how any such semigroup must be a family of exponentials generated by a bounded sublinear rate operator.