On reflected diffusions in cones and cylinders
Oleksii Kulyk, Andrey Yurievich Pilipenko, Sylvie Rœlly · Ukrains’kyi Matematychnyi Zhurnal · 2023
UDC 519.21 Let X be a diffusion in a cone with oblique reflection at the boundary. We study the question whether X reaches a vertex of the cone for a finite time with positive probability. We propose new probabilistic method of investigation connected with the long-term behavior of a diffusion reflected in a cylinder.