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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-15,
author = {Giovanni Peccati and Marc Yor},
title = {Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {235-250},
zbl = {1116.60013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-15}
}
Giovanni Peccati; Marc Yor. Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections. Banach Center Publications, Tome 72 (2006) pp. 235-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-15/