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A critical case for Brownian slow points
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  • Published: March 1996

A critical case for Brownian slow points

  • Richard F. Bass1 &
  • Krzysztof Burdzy1 

Probability Theory and Related Fields volume 105, pages 85–108 (1996)Cite this article

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  • 2 Citations

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Summary

LetX t be a Brownian motion and letS(c) be the set of realsr≧0 such that üX r+t −X r ü≦c√t, 0≦t≦h, for someh=h(r)>0. It is known thatS(c) is empty ifc<1 and nonempty ifc>1, a.s. In this paper we prove thatS(1) is empty a.s.

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Author information

Authors and Affiliations

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

    Richard F. Bass & Krzysztof Burdzy

Authors
  1. Richard F. Bass
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  2. Krzysztof Burdzy
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Additional information

This research was partially supported by NSF Grant 9322689.

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Cite this article

Bass, R.F., Burdzy, K. A critical case for Brownian slow points. Probab. Th. Rel. Fields 105, 85–108 (1996). https://doi.org/10.1007/BF01192072

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  • Received: 07 June 1995

  • Issue Date: March 1996

  • DOI: https://doi.org/10.1007/BF01192072

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Mathematics Subject Classification (1991)

  • 60G17
  • 60J65
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