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# Cutting Brownian Paths

 dc.contributor.author Burdzy, Krzysztof dc.contributor.author Bass, Richard F. dc.date.accessioned 2005-11-16T17:24:23Z dc.date.available 2005-11-16T17:24:23Z dc.date.issued 1999-01 dc.identifier.citation Burdzy, K. & R. Bass. Cutting Brownian paths. In Memoir AMS, 137(657). Providence, RI: American Mathematical Society, 1999. en dc.identifier.uri http://hdl.handle.net/1773/2159 dc.description 99 pages. en dc.description.abstract Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line en 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). dc.description.sponsorship Research partially supported by NSF grant DMS-9322689. en dc.format.extent 547503 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher American Mathematical Society en dc.relation.ispartofseries Memoirs AMS;vol. 137 number 657 dc.subject Planar Brownian motion en dc.subject cut lines en dc.subject cut points en dc.subject exceptional sets en dc.subject Taylor’s problem en dc.subject Bessel processes en dc.subject conditioned Brownian motion en dc.subject cones en dc.subject random walks en dc.subject wedges en dc.subject points of increase en dc.subject convex hull en dc.title Cutting Brownian Paths en dc.type Article en
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