Cut Points on Brownian Paths
نویسندگان
چکیده
Let X be a standard 2-dimensional Brownian motion. There exists a.s. t ∈ (0, 1) such that X([0, t)) ∩ X((t, 1]) = ∅. It follows that X([0, 1]) is not homeomorphic to the Sierpiński carpet a.s.
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Geometric and Fractal Properties of Brownian Motion and Random Walk Paths in Two and Three Dimensions
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