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arXiv · 1803.10613

Minkowski content of Brownian cut points

Nina Holden·Gregory F. Lawler·Xinyi Li·Xin Sun
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Abstract

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.

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Nina Holden, Gregory F. Lawler, Xinyi Li, Xin Sun. 2018-03-28. Minkowski content of Brownian cut points. https://arxiv.org/abs/1803.10613

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