Corpus ID: 67837710

# Minkowski content of Brownian cut points

@article{Holden2018MinkowskiCO,
title={Minkowski content of Brownian cut points},
author={N. Holden and G. Lawler and X. Li and X. Sun},
journal={arXiv: Probability},
year={2018}
}
• N. Holden, +1 author X. Sun
• Published 2018
• Mathematics
• arXiv: Probability
• Let $W(t)$, $0\leq t\leq T$, be a Brownian motion in $\mathbb{R}^d$, $d=2,3$. We say that $x$ is a cut point for $W$ if $x=W(t)$ for some $t\in(0,T)$ such that $W [0,t)$ and $W (t,T]$ are disjoint. In this work, we prove that a.s. the Minkowski content of the set of cut points for $W$ exists and is finite and non-trivial.