Let (µn : n = 0) be Borel probabilities on a metric space S such that µn - µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn - µn for all n and Xn - X0 in probability. By Skorohod's theorem, Skorohod...

Let (µn : n = 0) be Borel probabilities on a metric space S such that µn - µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn - µn for all n and Xn - X0 in probability. By Skorohod’s theorem, Skorohod...

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 =...