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

Giovanni Peccati (1) , Marc Yor (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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).

Mots clés: Brownian sheet; Quadratic functionals; Watson's identity

Domaines: Probabilités [math.PR]

Giovanni Peccati, Marc Yor. "Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections". 2005. ⟨hal-00004092⟩