Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
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
Published electronically: August 4, 2009
MathSciNet review: 2446851
Full-text PDF

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 $ \varphi$-sub-Gaussian stochastic processes.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G07, 42C40

Retrieve articles in all journals with MSC (2000): 60G07, 42C40


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: http://dx.doi.org/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): May 17, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society