Minkowski content of Brownian cut points

Nina Holden, Gregory F. Lawler, Xinyi Li, Xin Sun

Research output: Contribution to journalArticlepeer-review


Let W(t), 0 ≤ t ≤ T , be a Brownian motion in Rd , d = 2, 3. We say that x is a cut point for W if x = W(t) for some t ∈ (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.

Original languageEnglish (US)
Pages (from-to)455-488
Number of pages34
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
StatePublished - Feb 2021


  • Brownian motion
  • Cut point
  • Minkowski content

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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