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

Approximation of $ \operatorname{SSub}_{\varphi}(\Omega)$ stochastic processes in the space $ L_{p}(\mathbb{T})$


Authors: Yu. V. Kozachenko and O. E. Kamenshchikova
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 83-88
MSC (2000): Primary 60G17; Secondary 60G07
Published electronically: December 29, 2009
MathSciNet review: 2494537
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Abstract: A bound for the distributions of norms is obtained for $ \operatorname{Sub}_{\varphi}(\Omega)$ stochastic processes in the space $ L_{p}(\mathbb{T})$. This bound is used to construct an approximation of strictly $ \varphi$-sub-Gaussian processes by random broken lines in the space $ L_{p}(\mathbb{T})$ with a given accuracy and reliability


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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

O. E. Kamenshchikova
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: kamalev@gmail.com

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00782-0
PII: S 0094-9000(09)00782-0
Keywords: Approximation, $ {SSub}_{\varphi }(\Omega )$ process, interpolating broken line
Received by editor(s): November 5, 2007
Published electronically: December 29, 2009
Article copyright: © Copyright 2009 American Mathematical Society