Uniformly continuous semigroups of sublinear transition operators

In this work we investigate uniformly continuous semigroups of sublinear transition operators on the Banach space of bounded real-valued functions on some countable set. We show how such a semigroup can be retrieved as the solution to an abstract Cauchy problem by showing that it is equal to the family of exponentials generated by a so-called bounded sublinear rate operator. We also show that given any bounded sublinear rate operator, the family of corresponding exponentials forms such a semigroup. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/122/abstr.html