A Skorohod Representation Theorem for Uniform Distance - Patrizia Berti; Luca Pratelli; Pietro Rigo (Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ), 2010)
Let µn be a probability measure on the Borel sigma-field on D[0, 1] with respect to Skorohod distance, n = 0. Necessary and sufficient conditions for the following statement are provided. On some probability space, there are D[0, 1]-valued random variables Xn such that Xn tilde µn for all n = 0 and ||Xn - X0|| –> 0 in probability, where ||·|| is the sup-norm. Such conditions do not require µ0 separable under ||·||. Applications to exchangeable empirical processes and to pure jump processes are given as well.
Keywords: 330; Cadlag function Exchangeable empirical process Separable probability measure Skorohod representation theorem Uniform distance Weak convergence of probability measures