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
Asymptotics of the generating function for the volume of the Wiener sausage
Download PDF
Download PDF
  • Published: September 1994

Asymptotics of the generating function for the volume of the Wiener sausage

  • Michiel van den Berg1 &
  • Erwin Bolthausen2 

Probability Theory and Related Fields volume 99, pages 389–397 (1994)Cite this article

  • 112 Accesses

  • 7 Citations

  • Metrics details

Summary

We consider the generating function\(\mathbb{E}\exp (\lambda |C_\varepsilon (t)|)\) of the voltime of the Wiener sausageC ∈ (t), which is the ε-neighbourhood of the Wiener path in the time interval [0,t]. For γ<0, the limiting behavior fort→∞, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For γ>0 it had been investigated by van den Berg and Tóth, but in contrast to the case γ<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large γ.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. van den Berg, M., Tóth, B.: Expontetial estimates for the Wiener sausage. Probab. Theory Relat. Fields88, 249–259 (1991)

    Google Scholar 

  2. Spitzer, F.: Electrostatic capacity, heat flow and Brownian motion. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 110–121 (1964)

    Google Scholar 

  3. Sznitman, A.S.: Some bounds and limiting results for the measure of Wiener sausage of small radius associated with elliptic diffusions. Stochastic Processes Appl.25, 1–25 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton, EH14 4AS, Edinburgh, UK

    Michiel van den Berg

  2. Institut für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Erwin Bolthausen

Authors
  1. Michiel van den Berg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erwin Bolthausen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

van den Berg, M., Bolthausen, E. Asymptotics of the generating function for the volume of the Wiener sausage. Probab. Th. Rel. Fields 99, 389–397 (1994). https://doi.org/10.1007/BF01199898

Download citation

  • Received: 02 February 1993

  • Revised: 03 January 1994

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01199898

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 (1994)

  • 60J65
  • 60F10
  • 60J45
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