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

Giovanni Peccati, and Marc Yor. "Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections." Banach Center Publications 72.1 (2006): 235-250. <http://eudml.org/doc/282084>.

@article{GiovanniPeccati2006,
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).},
author = {Giovanni Peccati, Marc Yor},
journal = {Banach Center Publications},
keywords = {Brownian sheet; quadratic functionals; Watson's identity},
language = {eng},
number = {1},
pages = {235-250},
title = {Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections},
url = {http://eudml.org/doc/282084},
volume = {72},
year = {2006},
}

TY - JOUR
AU - Giovanni Peccati
AU - Marc Yor
TI - Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 235
EP - 250
AB - 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).
LA - eng
KW - Brownian sheet; quadratic functionals; Watson's identity
UR - http://eudml.org/doc/282084
ER -