Skip to main content

Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods

Part of the Lecture Notes in Mathematics book series (LNM,volume 1158)

Keywords

  • Brownian Motion
  • Riemannian Manifold
  • Scalar Curvature
  • Harmonic Measure
  • Exit Time

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Airault and H. Follmer, Relative densities of semimartingales, Inventiones Mathematicae, 27 (1974), 299–327.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. K.B. Athreya and T.G. Kurtz, A generalization of Dynkin's identity, Annals of Probability 1 (1973), 570–579.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E.B. Dykin, Markov Processes, 2 vols., Springer Verlag, New York, Berlin, Heidelberg, 1965.

    CrossRef  Google Scholar 

  4. A. Gray, L. Karp, M. Pinsky, The mean exit time from a tubular neighborhood in a Riemannian manifold (in preparation).

    Google Scholar 

  5. A. Gray and M. Pinsky, The mean exit time from a small geodesic ball in a Riemannian manifold, Bulletin des Sciences Mathematiques 107 (1983), 345–370.

    MathSciNet  MATH  Google Scholar 

  6. A. Gray and T.J. Willmore, Mean Value Theorems on Riemannian manifolds, Proc. Royal Soc. Edinburgh 92A (1982), 343–364.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. M. Pinsky, Moyenne stochastique sur une variete Riemannienne, Comptes Rendus Acad. Sciences. Paris 292 (1981), 991–994.

    MathSciNet  MATH  Google Scholar 

  8. M. Pinsky, Brownian motion in a small geodesic ball, to appear in Asterisque, 1984, Proceedings of the Colloque Laurent Schwartz.

    Google Scholar 

  9. M. Pinsky, The mean exit time of a diffusion process from a small sphere, Proceedings of the Amer. Math. Soc., 1984, to appear.

    Google Scholar 

  10. M. Pinsky, On non-Euclidean harmonic measure, Annales de l'Institut Henri Poincaré 1985, to appear.

    Google Scholar 

  11. Y. Takahashi and S. Watanabe, The Onsager-Machlup function of diffusion processes, in Stochastic Integrals, Springer Verlag Lecture Notes in Mathematics, vol. 851 1981, 433–463.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Pinsky, M.A. (1986). Mean exit times and hitting probabilities of Brownian motion in geodesic balls and tubular neighborhoods. In: Albeverio, S.A., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080220

Download citation

  • DOI: https://doi.org/10.1007/BFb0080220

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15998-8

  • Online ISBN: 978-3-540-39703-8

  • eBook Packages: Springer Book Archive