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

Authors:
Yu. V. Kozachenko and E. V. Turchin

Translated by:
O. I. Klesov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **78** (2008).

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 -sub-Gaussian stochastic processes.

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Additional Information

**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:
https://doi.org/10.1090/S0094-9000-09-00764-9

Keywords:
Wavelets,
$\varphi $-sub-Gaussian stochastic processes

Received by editor(s):
May 17, 2007

Published electronically:
August 4, 2009

Article copyright:
© Copyright 2009
American Mathematical Society