A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field. (6th May 2018) - Ai, Xiaohui
Abstract : The bivariate Brownian bridge, a nontensor Gaussian Field, is defined by B ( t 1, t 2 ) = W ( t 1, t 2 ) W ( 1, 1 ) = 0 = W ( t 1, t 2 ) - t 1 t 2 W ( 1, 1 ), where t 1, t 2 ∈ I = [ 0, 1 ] and W ( t 1, t 2 ) is a Brownian sheet. We obtain a distributional identity, a consequence of the Karhunen-Loève expansion for the bivariate Brownian bridge by Fredholm integral equation and Laplace transform approach.