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
Upper classes for the increments of fractional Wiener processes
Download PDF
Download PDF
  • Published: September 1989

Upper classes for the increments of fractional Wiener processes

  • J. Ortega1 

Probability Theory and Related Fields volume 80, pages 365–379 (1989)Cite this article

  • 65 Accesses

  • 10 Citations

  • Metrics details

Summary

Let (X(t), t≧0) be a centred Gaussian process with stationary increments andEX 2 (t)=C 0 t 2α for someC 0>0, 0<α<1, and let 0<a t ≦t be a nondecreasing function oft witha t /t nonincreasing. The asymptotic behaviour of several increment processes constructed fromX anda t is studied in terms of their upper classes.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Berman, S.M.: Limit theorems for the maximum term in stationary sequences. Ann. Math. Statist.35, 502–516 (1964)

    Google Scholar 

  2. Berman, S.M.: An asymptotic bound for the distribution of the maximum of a Gaussian process. Ann. Inst. Henri Poincaré21, 47–57 (1985)

    Google Scholar 

  3. Berman, S.M.: The maximum of a Gaussian process with nonconstant variance. Ann. Inst. Henri Poincaré21, 383–391 (1985)

    Google Scholar 

  4. Csörgö, M., Révész, P.: How big are the increments of the Wiener process?. Ann. Probab.7, 731–743 (1979)

    Google Scholar 

  5. Orey, S.: Growth rate of certain Gaussian processes. In: Proc. Sixth Berkeley, Symposium Math. Stat. Prob., vol. 2, pp. 443–451. Berkeley: University of California Press 1971

    Google Scholar 

  6. Ortega, J., Wschebor, M.: On the increments of the Wiener process. Z. Wahrscheinlichkeitstheor. Verw. Geb.65, 329–339 (1984)

    Google Scholar 

  7. Ortega, J.: On the size of the increments of non-stationary Gaussian processes. Stochastic Proc. Appl.18, 47–56 (1984)

    Google Scholar 

  8. Ortega, J.: Comportamiento asintótico de los incrementos de los procesos de Wiener fraccionarios. Actas II Congreso Latinoamericano Prob. Est. Mat., pp. 195–215, Caracas: Equinoccio 1986

    Google Scholar 

  9. Plackett, R.L.: A reduction formula for normal multivariate integrals. Biometrika41, 351–360 (1954)

    Google Scholar 

  10. Qualls, C., Watanabe, H.: Asymptotic properties of Gaussian processes. Ann. Math. Statist.43, 580–596 (1972)

    Google Scholar 

  11. Qualls, C., Watanabe, H.: Asymptotic properties of Gaussian random fields. Trans. Am. Math. Soc.177, 155–171 (1973)

    Google Scholar 

  12. Rényi, A.: Probability theory. Amsterdam: North-Holland 1970

    Google Scholar 

  13. Révész, P.: On the increments of Wiener and related processes. Ann. Probab.10, 613–627 (1982)

    Google Scholar 

  14. Slepian, D.: The one-sided barrier problem for Gaussian noise. Bell System Tech. J.41, 463–501 (1962)

    Google Scholar 

  15. Watanabe, H.: An asymptotic property of Gaussian processes. Trans. Am. Math. Soc.148, 233–248 (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Depto. de Matemáticas, Instituto Venezolano de Investigaciones Cientificas, Apartado 21.827, 1020-A, Caracas, Venezuela

    J. Ortega

Authors
  1. J. Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially financed by CONICIT, Proyecto S1-1372. This work was completed while the author was visiting the Université de Paris-Sud, Orsay, France

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ortega, J. Upper classes for the increments of fractional Wiener processes. Probab. Th. Rel. Fields 80, 365–379 (1989). https://doi.org/10.1007/BF01794429

Download citation

  • Received: 01 June 1987

  • Revised: 24 February 1988

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF01794429

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

  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • Mathematical Biology
  • Gaussian Process
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