Integral expression for the stationary distribution of reflected Brownian motion in a wedge

Abstract : For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary distribution (when it exists), in terms of Cauchy integrals and generalized Chebyshev polyno-mials. To that purpose we solve a Carleman-type boundary value problem on a hyperbola, satisfied by the Laplace transforms of the boundary stationary distribution.
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Pré-publication, Document de travail
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Contributeur : Sandro Franceschi <>
Soumis le : vendredi 15 février 2019 - 10:17:58
Dernière modification le : lundi 18 mars 2019 - 16:09:21