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On hardly visited points of the Brownian motion
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  • Published: March 1992

On hardly visited points of the Brownian motion

  • Antónia Földes1 &
  • Pál Révész2 

Probability Theory and Related Fields volume 91, pages 71–80 (1992)Cite this article

  • 76 Accesses

  • 6 Citations

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Summary

LetL(x, t) be the local time process of a standard Wiener process {W(t),t>0}. Denote

$$\begin{gathered} T_r = \inf \left\{ {t > 0;L\left( {0,t} \right) \geqq r} \right\}, \hfill \\ \mu \left( {r,q} \right) = \mu \left( {y;0< L\left( {y,T_r } \right)< q} \right) \hfill \\ \end{gathered} $$

, The almost sure behavior of the random measure μ(r, q) is investigated.

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References

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Author information

Authors and Affiliations

  1. The College of Staten Island, The City University of New York, 10301, Staten Island, NY, USA

    Antónia Földes

  2. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Pál Révész

Authors
  1. Antónia Földes
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  2. Pál Révész
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Cite this article

Földes, A., Révész, P. On hardly visited points of the Brownian motion. Probab. Th. Rel. Fields 91, 71–80 (1992). https://doi.org/10.1007/BF01194490

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  • Received: 23 August 1990

  • Revised: 04 June 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01194490

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Keywords

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