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arXiv · 1703.09433

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

Sandro Franceschi·Kilian Raschel
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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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Sandro Franceschi, Kilian Raschel. 2020-06-09. Integral expression for the stationary distribution of reflected brownian motion in a wedge. https://doi.org/10.3150/19-bej1107

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