Corpus ID: 67837710

Minkowski content of Brownian cut points

  title={Minkowski content of Brownian cut points},
  author={N. Holden and G. Lawler and X. Li and X. Sun},
  journal={arXiv: Probability},
  • N. Holden, G. Lawler, +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. 

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