Cutting Brownian Paths

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Cutting Brownian Paths

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Title: Cutting Brownian Paths
Author: Burdzy, Krzysztof; Bass, Richard F.
Abstract: Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line L is a cut line if there exists a time t [is an element of the set] (0, 1) such that the trace of {Z [subscript] s : 0 [is less than or equal to] s < t} lies on one side of L and the trace of {Z [subscript] s : t < s < 1} lies on the other side of L. In this paper we prove that with probability one cut lines do not exist. This provides a solution to Problem 8 in Taylor (1986).
Description: 99 pages.

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