We supposeK(w) to be the boundary of the closed convex hull of a sample path ofZ t(w), 0 ≦t ≦ 1 of Brownian motion ind-dimensions. A combinatorial result of Baxter and Borndorff Neilson on the convex hull of a random walk, and a limiting process utilizing results of P. Levy on the continuity properties ofZ t(w) are used to show that the curvature ofK(w) is concentrated on a metrically small set.
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Research received support from ONR under contract No. Nonr-2587(02).
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Kinney, J.R. Convex hull of Brownian motion ind-dimensions. Israel J. Math. 4, 139–143 (1966). https://doi.org/10.1007/BF02937459
- Brownian Motion
- Random Walk
- Convex Hull
- Meromorphic Function
- Sample Path