A Skorohod Representation Theorem for Uniform Distance

Patrizia Berti, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Department of Mathematics, University of Modena and Reggio Emilia
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 109, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: 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: Cadlag; function; –; Exchangeable; empirical; process; –; Separable; probability; measure; –; Skorohod; representation; theorem–; Uniform; distance; –; Weak; convergence; of; probability; measures. (search for similar items in EconPapers)
Pages: 13 pages
Date: 2010-01
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