On reflected diffusions in cones and cylinders

Oleksii  Kulyk; Andrey Pilipenko; Sylvie Rœlly

doi:10.3842/umzh.v75i11.7418

Oleksii Kulyk Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Poland
Andrey Pilipenko Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv and National Technical University of Ukraine ,,Igor Sikorsky Kyiv Polytechnic Institute''
Sylvie Rœlly Institut für Mathematik, Universität Potsdam, Germany

DOI: https://doi.org/10.3842/umzh.v75i11.7418

Keywords: Reflected diffusion; Diffusion in a cone; Oblique reflection

Abstract

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.

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