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Ukrainian Mathematical Journal

, Volume 58, Issue 10, pp 1517–1537 | Cite as

Random processes in Sobolev-Orlicz spaces

  • Yu. V. Kozachenko
  • T. O. Yakovenko
Article
  • 20 Downloads

Abstract

We establish conditions under which the trajectories of random processes from Orlicz spaces of random variables belong with probability one to Sobolev-Orlicz functional spaces, in particular to the classical Sobolev spaces defined on the entire real axis. This enables us to estimate the rate of convergence of wavelet expansions of random processes from the spaces L p (Ω) and L 2 (Ω) in the norm of the space L q (ℝ).

Keywords

Random Process Orthonormal Basis Wavelet Analysis Orlicz Space Generalize Derivative 
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References

  1. 1.
    M. A. Krasnosel’skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
  2. 2.
    V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, American Mathematical Society, Providence, RI (2000).zbMATHGoogle Scholar
  3. 3.
    Yu. V. Kozachenko and T. O. Yakovenko, “Conditions under which random processes belong to some functional Orlicz spaces,” Visn. Kyiv. Univ., No. 5, 64–74 (2002).Google Scholar
  4. 4.
    W. Härdle, G. Kerkyacharian, D. Picard, and A. Tsybakov, Wavelets, Approximation and Statistical Applications, Springer, New York (1998).zbMATHGoogle Scholar
  5. 5.
    M. M. Rao and Z. D. Pen, Theory of Orlicz Spaces, Marcel Dekker, New York (1991).zbMATHGoogle Scholar
  6. 6.
    T. Yakovenko, “Conditions under which processes belong to Orlicz space in case of noncompact parametric set,” Theory Stochast. Proc., 10(26), Nos. 1–2, 178–183 (2004).Google Scholar
  7. 7.
    I. Daubechies, Ten Lectures on Wavelets, Soc. Ind. Appl. Math., Philadelphia (1992).zbMATHGoogle Scholar
  8. 8.
    C. K. Chui, An Introduction to Wavelets, Academic Press, New York (1992).zbMATHGoogle Scholar
  9. 9.
    Yu. V. Kozachenko, Lectures on Wavelet Analysis [in Ukrainian], TViMS, Kyiv (2004).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. V. Kozachenko
    • 1
  • T. O. Yakovenko
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyiv

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