Skip to main content
SpringerLink
Log in
Book cover

Séminaire de Probabilités XXIV 1988/89 pp 137–153Cite as

A zero-one law for integral functionals of the bessel process

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1426))

Abstract

In this paper, we find necessary and sufficient conditions for the finiteness of the integral functionals of the Bessel process: ∝ to f(Rs) ds, 0≤t<∞. They are in the form of a zero-one law and can be regarded as a counterpart of the They are in the form of a zero-one law and can be regarded as a counterpart of the Engelbert-Schmidt (1981) results, in the case of the Bessel process with dimension n≥2.

Research supported in part by the National Science Foundation under Grant DMS-87-23078, and in part by the U.S. Air Force Office of Scientific Research under Grant AFOSR-86-0203.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Engelbert, H.J. & Schmidt, W. (1981) On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations. Lecture Notes in Control and Information Sciences 36, 47–55. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  2. Engelbert, H. J. & Schmidt, W. (1985) 0-1-Gesetze für die Konvergenz von Integralfunktionalen gewisser semimartingale. Math. Nachr. 123, 177–185.

    Article  MathSciNet  MATH  Google Scholar 

  3. Engelbert, H. J. & Schmidt, W. (1987) On the Behaviour of Certain Bessel Functionals. An Application to a class of Stochastic Differential Equations. Math. Nachr. 131, 219–234.

    Article  MathSciNet  MATH  Google Scholar 

  4. Jeulin, T. (1982) Sur la convergence absolue de certaines integrales. In Séminaire de Probabilités XVI. Lecture Notes in Mathematics 920, 248–255. Springer-Verlag, Berlin.

    Google Scholar 

  5. Karatzas, I. & Shreve, S. E. (1987) Brownian Motion and Stochastic Calculus. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  6. Le Gall, J. F. (1985) Sur la mesure de Hausdorff de la courbe brownienne. In Séminaire de Probabilités XIX. Lecture Notes in Mathematics 1123, 297–313. Springer-Verlag, Berlin.

    Google Scholar 

  7. Pitman, J.W. & Yor, M. (1986) Some divergent integrals of Brownian motion. Analytic and Geometric Stochastics. Supplement to the journal Adv. Appl. Probability 18 (December 1986), 109–116.

    MathSciNet  MATH  Google Scholar 

  8. Ray, D. (1963) Sojourn times of diffusion processes. Illinois J. Math. 7, 615–630.

    MathSciNet  MATH  Google Scholar 

  9. Yor, M. (1978) Sur la continuité des temps locaux associés a certaines semimartingales. Astérisque 52–53, 23–35.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Columbia University, 10027, New York, N.Y.

    Xing-Xiong Xue

Authors
  1. Xing-Xiong Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jacques Azéma Marc Yor Paul André Meyer

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Xue, XX. (1990). A zero-one law for integral functionals of the bessel process. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIV 1988/89. Lecture Notes in Mathematics, vol 1426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083762

Download citation

  • DOI: https://doi.org/10.1007/BFb0083762

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52694-0

  • Online ISBN: 978-3-540-47098-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation