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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
DOI: https://doi.org/10.1090/S0094-9000-09-00782-0
Published electronically: December 29, 2009
MathSciNet review: 2494537
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Abstract | References | Similar Articles | Additional Information

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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  • 1. V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, TViMS, Kyiv, 1998; English transl., American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
  • 2. R. Guiliano Antonini, Yu. Kozachenko, and T. Nikitina, Spaces of $ \varphi$-sub-Gaussian random variables, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. XXVII (2003), no. 5, 95-124. MR 2056414 (2005f:60036)
  • 3. Yu. Kozachenko and E. I. Ostrovskiĭ, Banach spaces of random variables of sub-Gaussian type, Teor. Veroyatnost. i Mat. Statist. 32 (1985), 42-53; English transl. in Theory Probab. Math. Statist. 32 (1986), 45-56. MR 882158 (88e:60009)
  • 4. Yu. Kozachenko and Yu. A. Koval'chuk, Boundary value problems with random initial conditions, and function series of $ {Sub}_{\varphi}(\Omega)$. I, Ukrain. Mat. Zh. 50 (1998), no. 4, 504-515; English transl. in Ukrainian Math. J. 50 (1998), no. 4, 572-585. MR 1698149 (2000f:60029)

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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: https://doi.org/10.1090/S0094-9000-09-00782-0
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

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