Electron. J. Differential Equations, Vol. 2025 (2025), No. 122, pp. 1-26.

Uniformly continuous semigroups of sublinear transition operators

Alexander Erreygers

Abstract:
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.

Submitted September 26, 2025. Published December 30. 2025.
Math Subject Classifications: 47H20, 60G65, 47D07.
Key Words: Operator exponential; operator logarithm; imprecise Markov process; sublinear Markov process.
DOI: 10.58997/ejde.2025.122

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Alexander Erreygers
Foundations Lab for imprecise probabilities
Ghent University
Technologiepark-Zwijnaarde 125
9052 Ghent, Belgium
email: alexander.erreygers@ugent.be

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