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

Giovanni Peccati; Marc Yor

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

Giovanni Peccati·Marc Yor

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Abstract

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).

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Giovanni Peccati, Marc Yor. 2005-01-28. Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections. https://arxiv.org/abs/math/0501506

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