Levy's second arcsine law via the ballot theorem
Probability
2025-05-20 v1
Abstract
We provide a new and elementary proof of Levy's second arcsine law for Brownian motion. The only tools required are basic properties of Brownian motion and Poisson processes, and the ballot theorem. Our proof is readily extended to Brownian motion with drift.
Keywords
Cite
@article{arxiv.2505.12374,
title = {Levy's second arcsine law via the ballot theorem},
author = {Helmut H. Pitters},
journal= {arXiv preprint arXiv:2505.12374},
year = {2025}
}