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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 in probability of wavelet decompositions for stochastic processes from the space $ \operatorname{Exp}_{\varphi}(\Omega)$


Authors: Yu. V. Kozachenko and O. V. Polos’mak
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 85-99
MSC (2000): Primary 60G12, 42C40
Published electronically: January 20, 2011
MathSciNet review: 2667312
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Abstract: Conditions for the uniform convergence in probability on the interval $ [0,T]$ of wavelet decompositions of Orlicz stochastic processes of exponential type are found in the paper.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: yvk@univ.kiev.ua

O. V. Polos’mak
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: olgapolosmak@yandex.ru

DOI: http://dx.doi.org/10.1090/S0094-9000-2011-00812-5
PII: S 0094-9000(2011)00812-5
Keywords: Stochastic processes, wavelet decomposition, convergence in probability, Orlicz spaces
Received by editor(s): March 11, 2009
Published electronically: January 20, 2011
Additional Notes: This research was supported by the La Trobe University Research Grant #501821
Article copyright: © Copyright 2011 American Mathematical Society