Dual representations of Laplace transforms of Brownian excursion and generalized meanders

The Laplace transform of the d-dimensional distribution of Brownian excursion is expressed as the Laplace transform of the (d+1)-dimensional distribution of an auxiliary Markov process, started from a σ-finite measure and with the roles of arguments and times interchanged. A similar identity holds for the Laplace transform of a generalized Brownian meander, which is expressed as the Laplace transform of the same auxiliary Markov process, with a different initial law.