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Equivalent or absolutely continuous probability measures with given marginals

Author

Listed:
  • Berti Patrizia

    (Dipartimento di Matematica Pura ed Applicata ”G. Vitali”, Universita’ di Modena e Reggio-Emilia, via Campi 213/B, 41100 Modena, Italy)

  • Pratelli Luca

    (Accademia Navale, viale Italia 72, 57100 Livorno, Italy)

  • Rigo Pietro

    (Dipartimento di Matematica ”F. Casorati”, Universita’ di Pavia, via Ferrata 1, 27100 Pavia, Italy)

  • Spizzichino Fabio

    (Dipartimento di Matematica ”G. Castelnuovo”, Universita’ di Roma ”La Sapienza”, piazzale A. Moro 5, 00185 Roma, Italy)

Abstract

Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

Suggested Citation

  • Berti Patrizia & Pratelli Luca & Rigo Pietro & Spizzichino Fabio, 2015. "Equivalent or absolutely continuous probability measures with given marginals," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-12, May.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:12:n:4
    DOI: 10.1515/demo-2015-0004
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    References listed on IDEAS

    as
    1. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2014. "A unifying view on some problems in probability and statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 483-500, November.
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