3 papers
math.PR2026
Martin boundary of a degenerate Reflected Brownian Motion in a wedge
Maxence Petit
We consider an outward degenerate drifted Brownian motion in the quarter plane with oblique reflections on the boundaries. In this article, we explicitly compute the Laplace transf…
math.PR2025
On the Green's functions and Martin boundary structure of a planar diffusion in a discontinuous layered medium
Sandro Franceschi, Irina Kourkova, Maxence Petit
We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed…
math.PR2024
Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge
Sandro Franceschi, Irina Kourkova, Maxence Petit
We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green's functions is found in all directions. To this end,…