Theory of Probability and Mathematical Statistics

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

Author(s): Yu. V. Kozachenko; E. V. Turchin
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 78 (2008).
Journal: Theor. Probability and Math. Statist. No. 78 (2009), 83-95.
MSC (2000): Primary 60G07; Secondary 42C40
Posted: August 4, 2009
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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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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G07, 42C40

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: yvk@univ.kiev.ua

E. V. Turchin
Affiliation: Department of Higher Mathematics, Faculty for Mechanization of Agriculture, Dnipropetrovs'k State Agriculture University, Voroshilov Street 25, Dnipropetrovs'k, Ukraine
Email: evgturchyn@ukr.net

DOI: 10.1090/S0094-9000-09-00764-9
PII: S 0094-9000(09)00764-9
Keywords: Wavelets, $\varphi $-sub-Gaussian stochastic processes
Received by editor(s): 17/MAY/2007
Posted: August 4, 2009
Copyright of article: Copyright 2009, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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