Random processes in Sobolev-Orlicz spaces

  • Yu. V. Kozachenko
  • T. O. Yakovenko


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 $L_q(\mathbb{R})$.
How to Cite
Kozachenko, Y. V., and T. O. Yakovenko. “Random Processes in Sobolev-Orlicz Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 10, Oct. 2006, pp. 1340–1356, https://umj.imath.kiev.ua/index.php/umj/article/view/3537.
Research articles