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Copulae of probability measures on product spaces

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  • Scarsini, Marco

Abstract

It has been proved (Sklar, 1959, Publ. Inst. Statist. Univ. Paris 8 229-231) that any multivariate distribution function depends on its arguments only through its marginal distributions. An analogous result will be proved in the general framework of probability measures on (Polish) product spaces. Many properties, holding for distribution functions, still hold in the more general situation. Some results related to convergence in probability will be examined.

Suggested Citation

  • Scarsini, Marco, 1989. "Copulae of probability measures on product spaces," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 201-219, November.
    • Handle: RePEc:eee:jmvana:v:31:y:1989:i:2:p:201-219
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    Cited by:

    1. Embrechts, Paul & Puccetti, Giovanni, 2006. "Bounds for functions of multivariate risks," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 526-547, February.
    2. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    3. Jupp, P.E., 2015. "Copulae on products of compact Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 92-98.
    4. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    5. 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.
    6. Durante, Fabrizio & Fernández Sánchez, Juan & Trutschnig, Wolfgang, 2014. "Multivariate copulas with hairpin support," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 323-334.
    7. Xuan Vinh Doan & Karthik Natarajan, 2012. "On the Complexity of Nonoverlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 60(1), pages 138-149, February.

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