Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
Giovanni Peccati, Marc Yor (2006)
Banach Center Publications
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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).