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Perkkiö, Ari-Pekka ORCID logoORCID: https://orcid.org/0000-0002-9787-0330 und Treviño-Aguilar, Erick ORCID logoORCID: https://orcid.org/0000-0002-2543-8469 (2023): Michael Selections and Castaing Representations with càdlàg Functions. In: Set-Valued and Variational Analysis, Bd. 31, 12 [PDF, 1MB]

Abstract

It follows from Michael’s selection theory that a closed convex nonempty-valued mapping from the Sorgenfrey line to a euclidean space is inner semicontinuous if and only if the mapping can be represented as the image closure of right-continuous selections of the mapping. This article gives necessary and sufficient conditions for the representation to hold for càdlàg selections, i.e., for selections that are right-continuous and have left limits. The characterization is motivated by continuous time stochastic optimization problems over càdlàg processes. Here, an application to integral functionals of càdlàg functions is given.

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