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Geometric properties of 2-dimensional Brownian paths
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  • Published: May 1989

Geometric properties of 2-dimensional Brownian paths

  • Krzysztof Burdzy1 

Probability Theory and Related Fields volume 81, pages 485–505 (1989)Cite this article

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Summary

Let A be the set of all points of the plane ℂ, visited by 2-dimensional Brownian motion before time 1. With probability 1, all points of A are “twist points” except a set of harmonic measure zero. “Twist points” may be continuously approached in ℂ\A only along a special spiral. Although negligible in the sense of harmonic measure, various classes of “cone points” are dense in A, with probability 1. “Cone points” may be approached in ℂ\A within suitable wedges.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Krzysztof Burdzy

Authors
  1. Krzysztof Burdzy
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Additional information

Research supported in part by NSF Grant DMS 8419377

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Burdzy, K. Geometric properties of 2-dimensional Brownian paths. Probab. Th. Rel. Fields 81, 485–505 (1989). https://doi.org/10.1007/BF00367299

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  • Received: 05 June 1987

  • Revised: 15 August 1988

  • Issue Date: May 1989

  • DOI: https://doi.org/10.1007/BF00367299

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Statistical Theory
  • Geometric Property
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