Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
Probability
2007-05-23 v1
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).
Keywords
Cite
@article{arxiv.math/0501506,
title = {Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections},
author = {Giovanni Peccati and Marc Yor},
journal= {arXiv preprint arXiv:math/0501506},
year = {2007}
}