A random approximation of set valued càdlàg functions
A càdlàg (acronym for the French term: continue à\ droite, limite à\ gauche) function is a function continuous on the right with left limits. ``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 \(f_{n,m}\) is constructed (where \(n\) and \(m\) are the respective sample sizes). Under general conditions, rates of convergence are obtained for Skorokhod's \(J_1\) topology, and in case of continuity of the estimated function also for the uniform one.''
scientific article; zbMATH DE number 2117747