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

Sandro Franceschi; Kilian Raschel

doi:10.3150/19-BEJ1107

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

Sandro Franceschi
, Kilian Raschel

Université de Tours

Research output: Contribution to journal › Article › peer-review

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 Carlemantype boundary value problem on a hyperbola, satisfied by the Laplace transforms of the boundary stationary distribution.

Original language	English
Pages (from-to)	3673-3713
Number of pages	41
Journal	Bernoulli
Volume	25
Issue number	4 B
DOIs	https://doi.org/10.3150/19-BEJ1107
Publication status	Published - 1 Jan 2019

Keywords

Boundary value problem with shift
Carleman-type boundary value problem
Conformal mapping
Laplace transform
Reflected Brownian motion in a wedge
Stationary distribution

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10.3150/19-BEJ1107

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title = "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 polynomials. To that purpose, we solve a Carlemantype boundary value problem on a hyperbola, satisfied by the Laplace transforms of the boundary stationary distribution.",

keywords = "Boundary value problem with shift, Carleman-type boundary value problem, Conformal mapping, Laplace transform, Reflected Brownian motion in a wedge, Stationary distribution",

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AU - Raschel, Kilian

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AB - 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 Carlemantype boundary value problem on a hyperbola, satisfied by the Laplace transforms of the boundary stationary distribution.

KW - Boundary value problem with shift

KW - Carleman-type boundary value problem

KW - Conformal mapping

KW - Laplace transform

KW - Reflected Brownian motion in a wedge

KW - Stationary distribution

U2 - 10.3150/19-BEJ1107

DO - 10.3150/19-BEJ1107

M3 - Article

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VL - 25

SP - 3673

EP - 3713

JO - Bernoulli

JF - Bernoulli

IS - 4 B

ER -

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

Abstract

Keywords

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