English

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}
}
R2 v1 2026-06-23T14:59:56.121Z