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Weak Convergence of Laws on ℝ K with Common Marginals

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  • Alessio Sancetta

    (University of Cambridge)

Abstract

We present a result on topologically equivalent integral metrics as reported by Rachev (Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester, 1991) and Müller (J. Appl. Probab. 29, 429–443, 1997) that metrize weak convergence of laws with common marginals. This result is relevant for applications, as shown in a few simple examples.

Suggested Citation

  • Alessio Sancetta, 2007. "Weak Convergence of Laws on ℝ K with Common Marginals," Journal of Theoretical Probability, Springer, vol. 20(2), pages 371-380, June.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:2:d:10.1007_s10959-007-0096-8
    DOI: 10.1007/s10959-007-0096-8
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    References listed on IDEAS

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    1. Scarsini, Marco, 1989. "Copulae of probability measures on product spaces," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 201-219, November.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Rüschendorf, Ludger & de Valk, Vincent, 1993. "On regression representations of stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 183-198, June.
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