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November 2019 Integral expression for the stationary distribution of reflected Brownian motion in a wedge
Sandro Franceschi, Kilian Raschel
Bernoulli 25(4B): 3673-3713 (November 2019). DOI: 10.3150/19-BEJ1107

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 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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Sandro Franceschi. Kilian Raschel. "Integral expression for the stationary distribution of reflected Brownian motion in a wedge." Bernoulli 25 (4B) 3673 - 3713, November 2019. https://doi.org/10.3150/19-BEJ1107

Information

Received: 1 January 2018; Revised: 1 September 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110152
MathSciNet: MR4010969
Digital Object Identifier: 10.3150/19-BEJ1107

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

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4B • November 2019
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