A note on large deviations of random sets and random upper semicontinuous functions

Abstract

In this paper, we show a sufficient condition under which the law of sums of i.i.d. compact random sets in a separable type p Banach space (resp. compact random upper semicontimuous functions) satisfies large deviations if the law of sums of its corresponding convex hull of compact random sets(resp. quasiconcave envelope of compact random upper semicontimuous functions) satisfies large deviations. © 2013 Springer-Verlag.