An explicit Laplace transform for the unique stationary measure of positive recurrent reflecting Brownian motion in the half-plane is derived by solving a discontinuous Riemann boundary value problem using Sokhotski-Plemelj formulas, with local and asymptotic behavior obtained via Tauberian theorems
Grisvard,Elliptic problems in nonsmooth domains, Society for Industrial and Applied Mathematics
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Stationary Distribution of Brownian Motion in the Half-Plane with Two-sided Reflections
An explicit Laplace transform for the unique stationary measure of positive recurrent reflecting Brownian motion in the half-plane is derived by solving a discontinuous Riemann boundary value problem using Sokhotski-Plemelj formulas, with local and asymptotic behavior obtained via Tauberian theorems