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A Skorohod Representation Theorem for Uniform Distance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "A Skorohod Representation Theorem for Uniform Distance," Quaderni di Dipartimento 109, University of Pavia, Department of Economics and Quantitative Methods.
  • Handle: RePEc:pav:wpaper:109
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    File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/wpaper/q109.pdf
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    References listed on IDEAS

    as
    1. Berti, Patrizia & Pratelli, Luca & Rigo, Pietro, 2006. "Asymptotic behaviour of the empirical process for exchangeable data," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 337-344, February.
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