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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://dem-web.unipv.it/web/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.
    2. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2009. "Skorohod Representation Theorem Via Disintegrations," Quaderni di Dipartimento 104, University of Pavia, Department of Economics and Quantitative Methods.
    Full references (including those not matched with items on IDEAS)

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