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A representation of local time for Lipschitz surfaces
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  • Published: December 1990

A representation of local time for Lipschitz surfaces

  • Rodrigo Bañuelos1,
  • Richard F. Bass2 &
  • Krzysztof Burdzy2 

Probability Theory and Related Fields volume 84, pages 521–547 (1990)Cite this article

Summary

Suppose thatD ⊂ ℝn,n≧2, is a Lipschitz domain and letN t (r) be the number of excursions of Brownian motion insideD with diameter greater thanr which started before timet. ThenrN t (r) converges asr→0 to a constant multiple of local time on ∂D, a.s. and inL p for allp<∞. The limit need not exist or may be trivial (0 or ∞) in Hölder domains, non-tangentially accessible domains and domains whose boundaries have finite surface area.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Rodrigo Bañuelos

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

    Richard F. Bass & Krzysztof Burdzy

Authors
  1. Rodrigo Bañuelos
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  2. Richard F. Bass
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  3. Krzysztof Burdzy
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Additional information

The first author was supported by NSF Postdoctoral Fellowship

The second and third authors were supported in part by NSF grants DMS 8701073 and DMS 8702620

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Cite this article

Bañuelos, R., Bass, R.F. & Burdzy, K. A representation of local time for Lipschitz surfaces. Probab. Th. Rel. Fields 84, 521–547 (1990). https://doi.org/10.1007/BF01198318

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  • Received: 17 April 1989

  • Revised: 16 September 1989

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198318

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Local Time
  • Mathematical Biology
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