Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Brownian motion in a quasi-cone
Download PDF
Download PDF
  • Published: 12 April 2011

Brownian motion in a quasi-cone

  • Dante DeBlassie1 

Probability Theory and Related Fields volume 154, pages 127–148 (2012)Cite this article

  • 176 Accesses

  • 1 Citations

  • Metrics details

Abstract

We determine precise logarithmic asymptotics of the probability of a large exit time for Brownian motion in a quasi-cone. This answers a question formally posed by Lifshits and Shi (Bernoulli 8:745–765, 2002), but first studied by Li (Ann Probab 31:1078–1096, 2001).

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Bañuelos R., Carroll T.: Sharp integrability for Brownian motion in parabola-shaped regions. J. Funct. Anal. 218, 219–253 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bingham N.H., Goldie C.M., Teugels J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  3. Borodin A.N., Salminen P.: Handbook of Brownian Motion—Facts and Fromulae. Birkhäuser, Basel (1996)

    Book  Google Scholar 

  4. Burkholder D.L.: Exit times of Brownian motion, harmonic majorization and Hardy spaces. Adv. Math. 26, 182–205 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. DeBlassie R.D.: Exit times from cones in \({\mathbb{R}^n}\) . Probab. Theory Relat. Fields 74, 1–29 (1987)

    Article  MathSciNet  Google Scholar 

  6. DeBlassie D.: The exit place of Brownian Motion in an unbounded domain, to appear. Electron. J. Probab. 14, 2657–2690 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li W.: The first exit time of Brownian motion from an unbounded convex domain. Ann. Probab. 31, 1078–1096 (2001)

    Google Scholar 

  8. Lifshits M., Shi Z.: The first exit time of Brownian motion from a parabolic domain. Bernoulli 8, 745–765 (2002)

    MathSciNet  MATH  Google Scholar 

  9. Spitzer F.: Some theorems concerning 2-dimensional Brownian motion. Trans. Am. Math. Soc. 87, 187–197 (1958)

    MathSciNet  MATH  Google Scholar 

  10. Revuz D., Yor M.: Continuous Martingales and Brownian Motion. Springer, Berlin (1999)

    MATH  Google Scholar 

  11. Rogers L.C.G., Williams D.: Diffusions, Markov Processes, and Martingales, vol. 2, Itô Calculus. Wiley, Chichester (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, P. O. Box 30001, Department 3MB, Las Cruces, NM, 88003-8001, USA

    Dante DeBlassie

Authors
  1. Dante DeBlassie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dante DeBlassie.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

DeBlassie, D. Brownian motion in a quasi-cone. Probab. Theory Relat. Fields 154, 127–148 (2012). https://doi.org/10.1007/s00440-011-0364-5

Download citation

  • Received: 30 August 2010

  • Revised: 30 March 2011

  • Published: 12 April 2011

  • Issue Date: October 2012

  • DOI: https://doi.org/10.1007/s00440-011-0364-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Quasi-cone
  • Exit time
  • Regular variation
  • Maximal function
  • Exit place

Mathematics Subject Classification (2000)

  • Primary 60J65
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature