Skip to main content
SpringerLink
Log in

Functional Limit Theorems for the Increments of Gaussian Samples

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

Functional limit theorems for increments of Gaussian samples are obtained. As consequences, functional modulus of continuity theorem and functional large increment theorem of a fractional Brownian motion are established in this paper.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Chen M. Csörgő (2001) ArticleTitleA functional modulus of continuity for a Wiener process Stat. Probab. Lett. 51 215–223

    Google Scholar 

  2. M. Csörgő P. Révész (1981) Strong Approximations in Probability and Statistics Academic Press New York

    Google Scholar 

  3. A. Acosta Particlede (1983) ArticleTitleSmall deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm Ann. Probab. 11 78–101

    Google Scholar 

  4. V. Goodman J. Kuelbs (1991) ArticleTitleRate of clustering for some Gaussian self-similar processes Probab. Th. Rel. Fields 88 47–75

    Google Scholar 

  5. L. Gross (1970) Lectures in Modern Analysis and Applications II Lecture Notes in Math Vol 140. Springer Berlin

    Google Scholar 

  6. J. Kuelbs (1976) ArticleTitleA strong convergence theorem for Banach space valued random variables Ann. Probab. 4 744–771

    Google Scholar 

  7. J. Kuelbs W.V. Li M. Talagrand (1994) ArticleTitleLim inf results for Gaussian samples and Chung’s functional LIL Ann. Probab. 22 1879–1903

    Google Scholar 

  8. D. Monrad H. Rootzén (1995) ArticleTitleSmall values of Gaussian processes and functional laws of the iterated logarithm Probab. Th. Rel. Fields 101 173–192

    Google Scholar 

  9. C. Mueller (1981) ArticleTitleA unification of Strassen’s law and Lévy’s modulus of continuity Z. Wahrsch. Verw. Geb. 56 163–179

    Google Scholar 

  10. H. Oodaira (1972) ArticleTitleOn Strassen’s version of the law of the iterated for Gaussian processes Z. Wahrsch. Verw. Geb. 21 289–299

    Google Scholar 

  11. J. Ortega (1984) ArticleTitleOn the size of the increments of non-stationary Gaussian processes Stoch. Process. Appl. 18 47–56

    Google Scholar 

  12. P. Révész (1979) ArticleTitleA generalization of Strassen’s functional law of the iterated logarithm Z. Wahrsch. Verw. Geb 50 257–264

    Google Scholar 

  13. W. Wang (2001) ArticleTitleOn a functional limit result of increments of a fractional Brownian motion Acta Math. Hug. 93 153–170

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hangzhou Teacher’s College, 310012, Hangzhou

    Wensheng Wang

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Wensheng Wang

Authors
  1. Wensheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wensheng Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, W. Functional Limit Theorems for the Increments of Gaussian Samples. J Theor Probab 18, 327–343 (2005). https://doi.org/10.1007/s10959-005-3505-x

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10959-005-3505-x

Keywords

Search

Navigation