Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
Volume 72 / 2006
Banach Center Publications 72 (2006), 235-250
MSC: 60515, 60E10.
DOI: 10.4064/bc72-0-15
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).
