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Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann-Hilbert problem via Fourier transforms

Authors :
Fayolle, Guy
Franceschi, Sandro
Raschel, Kilian
Source :
Indagationes Mathematicae 2022
Publication Year :
2022

Abstract

The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the stationary distribution can indeed be found by solving a boundary value problem of the same kind as the one encountered in the quarter plane, up to various dualities and symmetries. The main idea is to start from Fourier (and not Laplace) transforms, allowing to get a functional equation for a single function of two complex variables.<br />Comment: 18 pages, 5 figures

Details

Database :
arXiv
Journal :
Indagationes Mathematicae 2022
Publication Type :
Report
Accession number :
edsarx.2206.12859
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.indag.2022.10.008