Dentcheva, Darinka
Differentable Selections of Set-Valued Mappings and Asymptotic Behavior of Random Sets in Infinite Dimensions
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

90C25 Convex programming

Abstract: We consider set-valued mappings acting between two linear normed spaces and having convex closed images. Our aim is to construct selections with directional differentiability properties up to the second order, using certain tangential approximations of the mapping. The constructions preserve measurability and lead to a directionally differentiable Castaing representation of measurable multifunctions admitting the required tangential approximation. A generalized set-valued central limit theorem for random sets in infinite dimensional spaces is presented. The results yield asymptotic distributions of measurable selections forming the Castaing representation of the multifunction.
Keywords: first- and secund-order differentiable set-valued mapping, selections, Wijsman topology, Castaing representation, central limit theorems