Geometric Deviation From L\'evy's Occupation Time Arcsine Law
Probability
2020-04-22 v1
Abstract
We prove a geometric extension of L\'evy's occupation time arcsine law near a hypersurface on a Riemannian manifold. The deviation from the classic arcsine law is of the order of the square-root of the time horizon and is expressed explicitly in terms of the mean curvature of the hypersurface and the local time of the underlying standard Brownian motion.
Cite
@article{arxiv.2004.10039,
title = {Geometric Deviation From L\'evy's Occupation Time Arcsine Law},
author = {Elton P. Hsu and Cheng Ouyang},
journal= {arXiv preprint arXiv:2004.10039},
year = {2020}
}