Abstract
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 language | English (US) |
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Pages (from-to) | 455-488 |
Number of pages | 34 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 58 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2021 |
Keywords
- Brownian motion
- Cut point
- Minkowski content
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty