Skip to main content

Levels at which every Brownian excursion is exceptional

  • Conference paper
  • First Online:
Séminaire de Probabilités XVIII 1982/83

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1059))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.V. Chacon, Y. Le Jan, E. Perkins, S.J. Taylor. Generalized arc length for Brownian motion and Lévy processes. Z.f.W. 57, 197–211 (1981).

    Article  MATH  Google Scholar 

  2. B. Davis. On Brownian slow points. Z.f.W. 64, 359–367 (1983).

    MathSciNet  MATH  Google Scholar 

  3. B. Davis, E. Perkins. Brownian slow points: the critical cases (preprint).

    Google Scholar 

  4. J. Dugundji. Topology. Boston, Allyn and Bacon, Inc., 1966.

    Google Scholar 

  5. J. Hawkes. A lower Lipschitz condition for the stable subordinator. Z.f.W. 17, 23–32 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Hawkes. On the Hausdorff dimension of the intersection of the range of a stable process with a Borel set. Z.f.W. 19, 90–102 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Hawkes. Hausdorff measure, entropy, and the independence of small sets. Proc. London Math. Soc. (3) 28, 700–724 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Hawkes, W.E. Pruitt. Uniform Dimension Results for Processes with Independent Increments. Z.f.W. 28, 277–288 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  9. K. Itô, H.P. McKean. Diffusion Processes and Their Sample Paths. Berlin-Heidelberg-New York, Springer, 1974.

    MATH  Google Scholar 

  10. J.-P. Kahane. Slow points of Gaussian processes. Conference on Harmonic Analysis in Honor of Antoni Zygmund, I, 67–83, Wadsworth, 1981.

    Google Scholar 

  11. F. B. Knight. Essentials of Brownian Motion and Diffusion. Amer. Math. Soc. Surveys 18, 1981.

    Google Scholar 

  12. P. Lévy. Processus Stochastiques et Mouvement Brownien. Paris, Gauthier-Villars, 1948.

    MATH  Google Scholar 

  13. E. Perkins. A global intrinsic characterization of Brownian local time. Ann. Probability 9, 800–817 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  14. E. Perkins. The exact Hausdorff measure of the level sets of Brownian motion. Z.f.W. 58, 373–388 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  15. E. Perkins. On the Hausdorff dimension of the Brownian slow points. Z.f.W. 64, 369–399 (1983).

    MathSciNet  MATH  Google Scholar 

  16. S. Orey, S.J. Taylor. How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. (3) 28, 174–192 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  17. P. Greenwood, E. Perkins. A conditioned limit theorem for random walk and Brownian local time on square root boundaries, Ann. Probability 11, 227–261 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  18. R.K. Getoor. The Brownian escape process. Ann. Probability 7, 864–867 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Williams. Path decompositions and continuity of local time for one-dimensional diffusions I. Proc. London Math. Soc. 28, 738–768 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  20. M. Emery, E. Perkins. On the filtration of B + L. Z.f.W. 59, 383–390 (1982).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. Azéma M. Yor

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Barlow, M.T., Perkins, E. (1984). Levels at which every Brownian excursion is exceptional. In: Azéma, J., Yor, M. (eds) Séminaire de Probabilités XVIII 1982/83. Lecture Notes in Mathematics, vol 1059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100028

Download citation

  • DOI: https://doi.org/10.1007/BFb0100028

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13332-2

  • Online ISBN: 978-3-540-38858-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics