Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/95323 
Erscheinungsjahr: 
2009
Schriftenreihe/Nr.: 
Quaderni di Dipartimento No. 104
Verlag: 
Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ), Pavia
Zusammenfassung: 
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 representation holds (with Xn -> X0 almost uniformly) if µ0 is separable. Two results are proved in this paper. First, Skorohod representation may fail if µ0 is not separable (provided, of course, non separable probabilities exist). Second, independently of µ0 separable or not, Skorohod representation holds if W(µn, µ0) -> 0 where W is Wasserstein distance (suitably adapted). The converse is essentially true as well. Such a W is a version of Wasserstein distance which can be defined for any metric space S satisfying a mild condition. To prove the quoted results (and to define W), disintegrable probability measures are fundamental.
Schlagwörter: 
Disintegration
Separable probability measure
Skorohod representation theorem
Wasserstein distance
Weak convergence of probability measures
Dokumentart: 
Working Paper

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