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Some exact equivalents for the Brownian motion in Hölder norm
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  • Published: December 1992

Some exact equivalents for the Brownian motion in Hölder norm

  • P. Baldi1 nAff2 &
  • B. Roynette2 

Probability Theory and Related Fields volume 93, pages 457–484 (1992)Cite this article

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  • 33 Citations

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Summary

Some exact equivalents of small probabilities are given for the Wiener measure on spaces of Hölder paths. It turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of Z. Ciesielski which makes the Brownian motion on these spaces easy to handle. In particular we study the equivalents of the probability of εB in a fixed ball, ofB in a small ball and we give applications to the speed of clustering in Strassen law.

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References

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Author information

Author notes
  1. P. Baldi

    Present address: Laboratoire de Probabilités, 4 Pl. Jussieu-Tour 56, F-75252, Paris, France

Authors and Affiliations

  1. Università di Tor Vergata, Via del Fontanile di Carcaricola, I-00133, Roma, Italy

    P. Baldi

  2. UER De Mathématique, Université de Nancy I, CO 140, F-54037, Nancy, France

    B. Roynette

Authors
  1. P. Baldi
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  2. B. Roynette
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Cite this article

Baldi, P., Roynette, B. Some exact equivalents for the Brownian motion in Hölder norm. Probab. Th. Rel. Fields 93, 457–484 (1992). https://doi.org/10.1007/BF01192717

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  • Received: 01 February 1991

  • Revised: 30 January 1992

  • Issue Date: December 1992

  • DOI: https://doi.org/10.1007/BF01192717

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Classical Result
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