In Electronic Journal of Differential Equations, 2025:122, Dec. 2025.
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.