• Bernoulli
  • Volume 25, Number 4B (2019), 3673-3713.

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

Sandro Franceschi and Kilian Raschel

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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 polynomials. 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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Bernoulli, Volume 25, Number 4B (2019), 3673-3713.

Received: January 2018
Revised: September 2018
First available in Project Euclid: 25 September 2019

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boundary value problem with shift Carleman-type boundary value problem conformal mapping Laplace transform reflected Brownian motion in a wedge stationary distribution


Franceschi, Sandro; Raschel, Kilian. Integral expression for the stationary distribution of reflected Brownian motion in a wedge. Bernoulli 25 (2019), no. 4B, 3673--3713. doi:10.3150/19-BEJ1107.

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