Bernoulli

  • 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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1569398781

Digital Object Identifier
doi:10.3150/19-BEJ1107

Mathematical Reviews number (MathSciNet)
MR4010969

Zentralblatt MATH identifier
07110152

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

Citation

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. https://projecteuclid.org/euclid.bj/1569398781


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