Conditions for the uniform convergence of expansions of 𝜑-sub-Gaussian stochastic processes in function systems generated by wavelets

Kozachenko, Yu.; Turchin, E. V.

doi:10.1090/S0094-9000-09-00764-9

Conditions for the uniform convergence of expansions of $\varphi$-sub-Gaussian stochastic processes in function systems generated by wavelets

Authors: Yu. V. Kozachenko and E. V. Turchin
Translated by: O. I. Klesov
Journal: Theor. Probability and Math. Statist. 78 (2009), 83-95
MSC (2000): Primary 60G07; Secondary 42C40
DOI: https://doi.org/10.1090/S0094-9000-09-00764-9
Published electronically: August 4, 2009
MathSciNet review: 2446851
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Abstract: The expansions with uncorrelated coefficients in function systems generated by wavelets are constructed in the paper for second order stochastic processes. Conditions for the uniform convergence with probability one on a finite interval are found for expansions whose coefficients are independent. Conditions for the uniform convergence in probability on a finite interval are found for expansions of strictly $\varphi$-sub-Gaussian stochastic processes.

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