Skip to main content
SpringerLink
Log in

On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. I

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish conditions under which there exists a function c(t) > 0 such that {fx1850-01}, where X(t) is a random process from an Orlicz space of random variables. We obtain estimates for the probabilities {fx1850-02}.

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. Yu. K. Belyaev, “On unboundedness of sample functions of Gaussian processes,” Teor. Ver. Primen., 3, Issue 3, 351–354 (1958).

    MathSciNet  Google Scholar 

  2. I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia (1992).

    MATH  Google Scholar 

  3. W. Härdle, G. Kerkyacharian, D. Picard, and A. Tsybakov, Wavelets, Approximation and Statistical Applications, Springer, New York (1998).

    MATH  Google Scholar 

  4. G. Walter and X. Shen, Wavelets and Other Orthogonal Systems, Chapman and Hall, London (2000).

    Google Scholar 

  5. Yu. V. Kozachenko, Lectures on Wavelet Analysis [in Ukrainian], TViMS, Kyiv (2004).

    MATH  Google Scholar 

  6. V. V. Buldygin and Yu. V. Kozachenko, Metric Characteristics of the Random Variables and Random Processes, American Mathematical Society, Providence, RI (2000).

    Google Scholar 

  7. Yu. V. Kozachenko, M. M. Perestyuk, and O. I. Vasylyk, “On uniform convergence of wavelet expansion of φ-sub-Gaussian random processes,” Random Oper. Stochast. Equat., 14, No. 3, 209–232 (2006).

    MATH  MathSciNet  Google Scholar 

  8. Yu. Kozachenko and E. Barrasa de la Krus, “Boundary-value problems for equations of mathematical physics with strictly Orlicz random initial conditions,” Random Oper. Stochast. Equat., 3, No. 3, 201–220 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  9. I. K. Matsak and A. N. Plichko, “Some inequalities for sums of independent random variables in Banach spaces,” Teor. Ver. Primen., 27, No. 3, 474–491 (1982).

    Google Scholar 

  10. M. Sh. Braverman, “Estimates for sums of independent random variables,” Ukr. Mat. Zh., 43, No. 2, 173–178 (1991).

    Article  MathSciNet  Google Scholar 

  11. Yu. Kozachenko, T. Sottinen, and O. Vasylyk, “Self-similar processes with stationary increments from the spaces {ie1850-01},” Teor. Imov. Mat. Statist., No. 65, 67–78 (2001).

    Google Scholar 

  12. K. O. Dzhaparidze and J. H. Zanten, “A series expansion of fractional Brownian motion,” Probab. Theory Rel. Fields, 130, 39–55 (2004).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    Yu. V. Kozachenko & M. M. Perestyuk

Authors
  1. Yu. V. Kozachenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1647–1660, December, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozachenko, Y.V., Perestyuk, M.M. On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. I. Ukr Math J 59, 1850–1869 (2007). https://doi.org/10.1007/s11253-008-0030-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0030-y

Keywords

Search

Navigation