Skip to main content

On the p-Lévy-Baxter property and its applications

  • 372 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1391)

Abstract

We consider the p-stable motion of index p (0<p<1) for which we establish the property analogous to the Lévy-Baxter one of the Brownian motion. We call this property the p-Lévy-Baxter property and using it we find a sufficient condition for perpendicularity of measures induced by the processes, which are Riemann-Stieltjes stochastic integrals with respect to the standard p-stable motions.

1980 Mathematics Subject Classification

  • 60G17
  • 60G30
  • Key words and phrases
  • p-stable motion (0<p<1)
  • modular functions of p-stable processes
  • perpendicularity of measures
  • Levy-Baxter type property

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   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
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. Baxter G., A strong limit theorem for Gaussian processes, Proc. Amer.Math.Soc. 7(1956) 522–527.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Billingsley P., Convergence of probability measures, John Wiley and Sons, Inc., New York-London-Sydney-Toronto, 1968.

    MATH  Google Scholar 

  3. Breiman L., Probability, Addison-Wesley Reading, Mass, 1968.

    MATH  Google Scholar 

  4. Feller W., An introduction to probability theory and its applications, vol.II, John Wiley and Sons, Inc., New York, 1966.

    MATH  Google Scholar 

  5. Lévy P., Le mouvement brownien plan, Amer.J.Math. 62(1940), 487–550.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Mijnheer J.L., Sample paths properties of stable processes, Math. Centre Tract.59 (1975).

    Google Scholar 

  7. Skorohod A.V., Asymptotic formulas for stable distribution laws, Selected Translations in Mathematical Statistics and Probabilityl, (1961), 157–161.

    Google Scholar 

  8. Slepian D., Some comments on the detection of Gaussian signals in Gaussian noise, IRE Trans.Inf.Th. 4(1958), 65–68.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Weron K., Relaxation in glassy materials from Levy stable distribution, Acta Physica Polonica 5 A70(1986).

    Google Scholar 

  10. Wichura M.J., Functional laws of the iterated logarithm for partial sums of i.i.d. random variables in the domain of attraction of a completely asymetric stable law, Ann.Probability 2(1974), 1108–1138.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Wong E., Stochastic processes in information and dynamical systems, McGraw-Hill, Inc., 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Mądrecki, A. (1989). On the p-Lévy-Baxter property and its applications. In: Cambanis, S., Weron, A. (eds) Probability Theory on Vector Spaces IV. Lecture Notes in Mathematics, vol 1391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083392

Download citation

  • DOI: https://doi.org/10.1007/BFb0083392

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51548-7

  • Online ISBN: 978-3-540-48244-4

  • eBook Packages: Springer Book Archive