Random processes in Sobolev-Orlicz spaces |
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Authors: | Yu V Kozachenko T O Yakovenko |
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Institution: | (1) Shevchenko Kyiv National University, Kyiv |
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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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1340–1356, October, 2006. |
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Keywords: | |
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