Arbeitspapier

Skorohod Representation Theorem Via Disintegrations

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.

Sprache
Englisch

Erschienen in
Series: Quaderni di Dipartimento ; No. 104

Klassifikation
Wirtschaft
Thema
Disintegration
Separable probability measure
Skorohod representation theorem
Wasserstein distance
Weak convergence of probability measures

Ereignis
Geistige Schöpfung
(wer)
Berti, Patrizia
Pratelli, Luca
Rigo, Pietro
Ereignis
Veröffentlichung
(wer)
Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ)
(wo)
Pavia
(wann)
2009

Handle
Letzte Aktualisierung
20.09.2024, 08:24 MESZ

Datenpartner

Dieses Objekt wird bereitgestellt von:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.

Objekttyp

  • Arbeitspapier

Beteiligte

  • Berti, Patrizia
  • Pratelli, Luca
  • Rigo, Pietro
  • Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ)

Entstanden

  • 2009

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