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Random processes in Sobolev-Orlicz spaces

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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).

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv

    Yu. V. Kozachenko & T. O. Yakovenko

Authors
  1. Yu. V. Kozachenko
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  2. T. O. Yakovenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1340–1356, October, 2006.

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Kozachenko, Y.V., Yakovenko, T.O. Random processes in Sobolev-Orlicz spaces. Ukr Math J 58, 1517–1537 (2006). https://doi.org/10.1007/s11253-006-0151-0

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  • DOI: https://doi.org/10.1007/s11253-006-0151-0

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