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
Conditioned Brownian motion in planar domains
Download PDF
Download PDF
  • Published: December 1995

Conditioned Brownian motion in planar domains

  • Richard F. Bass1 &
  • Krzysztof Burdzy1 

Probability Theory and Related Fields volume 101, pages 479–493 (1995)Cite this article

Summary

We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • [CZ] Chung, K.L., Zhao, Z.: Book in preparation

  • [Cr] Cranston, M.: Conditional Brownian motion, Whitney squares, and the conditional gauge theorem. In: Seminar of Stochastic Processes, 1988, pp. 109–119. Boston: Birkhäuser 1989

    Google Scholar 

  • [CFZ] Cranston, M., Fabes, E., Zhao, Z.: Conditional gauge and potential theory for the Schrödinger operator. Trans. Am. Math. Soc.307, 171–194 (1988)

    Google Scholar 

  • [CM] Cranston, M., McConnell, T.R.: The lifetime of conditioned Brownian motion. Z. Wahrscheinlichkeitstheor. Verw. Geb.65, 1–11 (1983)

    Google Scholar 

  • [Da] Dahlberg, B.: Estimates of harmonic measure. Arch. Rat. Mech. Anal.65, 275–288 (1977)

    Google Scholar 

  • [Dv] Davis, B.: Conditioned Brownian motion in planar domains. Duke Math. J.57, 397–421 (1988)

    Google Scholar 

  • [Do] Doob, J.L.: Classical Potential Theory and its Probabilistic Counterpart. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  • [McC] McConnell, T.R.: A conformal inequality related to the conditional gauge theorem. Trans. Am. Math. Soc.318, 721–733 (1990)

    Google Scholar 

  • [PS] Port, S.C., Stone, C.J.: Brownian Motion and Classical Potential Theory. New York: Academic Press 1978

    Google Scholar 

  • [Zh] Zhao, Z.: Green functions and conditioned gauge theorem for a two dimensional domain. In: Seminar on Stochastic Processes, 1987, pp. 283–294. Boston: Birkhäuser 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, Washington, USA

    Richard F. Bass & Krzysztof Burdzy

Authors
  1. Richard F. Bass
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krzysztof Burdzy
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by NSF grant DMS-9100244 and an AMS Centennial Fellowship

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bass, R.F., Burdzy, K. Conditioned Brownian motion in planar domains. Probab. Th. Rel. Fields 101, 479–493 (1995). https://doi.org/10.1007/BF01202781

Download citation

  • Received: 13 December 1993

  • Revised: 06 October 1994

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01202781

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

Mathematics Subject Classification (1985)

  • 60J50
  • 60J45
  • 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