Displaying similar documents to “Bounded Laws of the Iterated Logarithm for Quadratic Forms in Gaussian Random Variables.”

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).