Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections

Tom 72 / 2006

Giovanni Peccati, Marc Yor Banach Center Publications 72 (2006), 235-250 MSC: 60515, 60E10. DOI: 10.4064/bc72-0-15


We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated identity in law, involving the path variance of a Brownian bridge, due to Watson (1961). The proof is based on ideas from a recent note by J.-R. Pycke (2005) and on the stochastic Fubini theorem for general Gaussian measures proved in Deheuvels et al. (2004).


  • Giovanni PeccatiLaboratoire de Statistique Théorique et Appliquée
    Université Paris VI
    175, rue du Chevaleret
    75013 Paris, France
  • Marc YorLaboratoire de Probabilités et Modèles Aléatoires
    Universités Paris VI and Paris VII
    Paris, France
    Institut Universitaire de France

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