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math.PR2026
How to Study Reflected Brownian Motion in a Quadrant via Kernel Functional Equations? A short survey
Sandro Franceschi
We survey a line of works studying semimartingale reflected Brownian motion in a quadrant, covering both the non-degenerate and degenerate settings. Two main situations are emphasi…
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,…