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Sojourns and future infima of planar Brownian motion
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  • Published: September 1995

Sojourns and future infima of planar Brownian motion

  • Y. Hu1 &
  • Z. Shi2 

Probability Theory and Related Fields volume 103, pages 329–348 (1995)Cite this article

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Summary

Let {W(t); 0≦t≦1} be a two-dimensional Wiener process starting from 0. We are interested in the almost sure asymptotic behaviour, asr tends to 0, of the processesX(r) andY(r), whereX(r) denotes the total time spent byW in the ball centered at 0 with radiusr andY(r) the distance between 0 and the curve {W(t);r≦t≦1}. While a characterization of the lower functions ofY was previously established by Spitzer [S], we characterize via integral tests its upper functions as well as the upper and lower functions ofX.

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Authors and Affiliations

  1. Laboratoire de Probabilités, CNRS URA 224, Université Paris VI, Tour 56, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Y. Hu

  2. L.S.T.A.-CNRS URA 1321, Université Paris VI, Tour 45-55, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Z. Shi

Authors
  1. Y. Hu
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  2. Z. Shi
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Hu, Y., Shi, Z. Sojourns and future infima of planar Brownian motion. Probab. Th. Rel. Fields 103, 329–348 (1995). https://doi.org/10.1007/BF01195478

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  • Received: 11 November 1994

  • Revised: 20 February 1995

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01195478

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Mathematics Subject Classification (1991)

  • 60J65
  • 60G17
  • 60F15
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