A generalization of the Karhunen-Loeve expansion of the Brownian bridge

In this paper we give the Karhunen-Loeve expansion of a centered Gaussian process whose covariance function depends on two parameters, including the covariance function of the Brownian bridge as a special case. A statistical application, related to the weighted uniform empirical process is provided. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.