On the Sobolev removability of the graph of one-dimensional Brownian motion
Abstract
Suppose that B is a one-dimensional Brownian motion, and let Γ={(t,Bt):t∈[0,1]} be the graph of B|[0,1]. We characterize the Sobolev removability properties of Γ by showing that Γ is almost surely not W1,p-removable for all p∈[1,∞) but is almost surely W1,∞-removable.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Graph Theory Research
Urbanization and City Planning
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 4
- Publication date
- 30 June 2026
- Language
- EN