2017
Том 69
№ 6

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Random processes in Sobolev-Orlicz spaces

Kozachenko Yu. V., Yakovenko T. O.

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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 $L_P({\Omega})$ and $L_2({\Omega})$ in the norm of the space $L_q(\mathbb{R})$.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 10, pp 1517-1537.

Citation Example: Kozachenko Yu. V., Yakovenko T. O. Random processes in Sobolev-Orlicz spaces // Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1340–1356.

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