Work

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

Year: 2019

Type: article

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.

Source: Bernoulli

DOI: 10.3150/19-bej1107

Authors: Sandro Franceschi, Kilian Raschel

Institutions: Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation, Université de Tours, Université d'Orléans, Centre National de la Recherche Scientifique, Institut Denis Poisson

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W2601416403

FWCI: 3.205

Cites: 57

Cited by: 21

Related to: 10