Skip to main content
SpringerLink
Log in

On Haar expansion of Riemann–Liouville process in a critical case

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We show that Haar-based series representation of the critical Riemann–Liouville process Rα with α =3/2 is rearrangement non-optimal in the sense of convergence rate in C[0, 1]. Bibliography: 10 titles.

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. A. Ayahe and W. Linde, "Series representations of fractional Gaussian processes by trigonometric and Haar systems," Eletronic J. Probab., 14, 2691-2719 (2009).

    Google Scholar 

  2. A. Ayache and M. S. Taqqu, “Rate optimality of wavelet series approximations of fractional Brownian motion,” J. Fourier Anal. Appl., 9, 451-471 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  3. K. Dzhaparidze and H. van Zanten, "Optimality of an explicit series expansion of the fractional Brownian sheet," Statist. Probab. Letters, 71, 295-301 (2005).

    Article  MATH  Google Scholar 

  4. H. Gilsing and T. Sottinen, "Power series expansions for fractional Brownian motions," Theory Stoch. Proc., 9(25), 38-49 (2003).

    MathSciNet  Google Scholar 

  5. E. Iglói, "A rate optimal trigonometric series expansion of the fractional Brownian motion," Eletronic J. Probab., 10, 1381-1397 (2005).

    Google Scholar 

  6. Th. Kuuhn and W. Linde, "Optimal series representation of fractional Brownian sheets," Bernoulli, 8, 669-696 (2002).

    MathSciNet  Google Scholar 

  7. M. A. Lifshits, Gaussian Random Functions, Kluwer (1995).

  8. M. A. Lifshits and T. Simon, "Small deviations for fractional stable processes," Ann. Inst. H. Poinaré, 41, 725-752 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Malyarenko, "An optimal series expansion of the multiparameter fractional Brownian motion," J. Theor. Probab., 21, 459-475 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Shak, "An optimal wavelet series expansion of the Riemann-Liouville process," J. Theor. Probab., 24, 1030-1057 (2009).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Peterburg State University, St. Petersburg, Russia

    M. A. Lifshits

Authors
  1. M. A. Lifshits
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Lifshits.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 171–180.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lifshits, M.A. On Haar expansion of Riemann–Liouville process in a critical case. J Math Sci 167, 531–536 (2010). https://doi.org/10.1007/s10958-010-9940-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-010-9940-y

Keywords

Search

Navigation