A random approximation of set valued càdlàg functions

In this paper we study the problem of estimating a càdlàg function f whose values are compact convex sets. For this purpose a random selection of points in the interval [0, 1] is considered and for each selected point x, a random sample in f (x). On the basis of this a sequence of approximants fn,m is constructed (where n and m are the respective sample sizes). Under general conditions, rates of convergence are obtained for Skorokhod’s J1 topology, and in case of continuity of the estimated function also for the uniform one.  2004 Elsevier Inc. All rights reserved