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
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
Full-text PDF Free Access
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
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- R. Giuliano Antonini, Yu. Kozachenko, and T. Nikitina, Spaces of $\phi $-sub-Gaussian random variables, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003), 95–124 (English, with English and Italian summaries). MR 2056414
- Yu. V. Kozachenko and E. I. Ostrovskiĭ, Banach spaces of random variables of sub-Gaussian type, Teor. Veroyatnost. i Mat. Statist. 32 (1985), 42–53, 134 (Russian). MR 882158
- Yu. V. Kozachenko and Yu. A. Koval′chuk, Boundary value problems with random initial conditions, and functional series from ${\rm sub}_\phi (\Omega )$. I, Ukraïn. Mat. Zh. 50 (1998), no. 4, 504–515 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 50 (1998), no. 4, 572–585 (1999). MR 1698149, DOI https://doi.org/10.1007/BF02487389
References
- 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)
- 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)
- 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)
- Yu. Kozachenko and Yu. A. Koval’chuk, Boundary value problems with random initial conditions, and function series of $\mathrm {Sub}_{\varphi }(\Omega )$. 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)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
60G17,
60G07
Retrieve articles in all journals
with MSC (2000):
60G17,
60G07
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
Keywords:
Approximation,
$\mathrm {SSub}_{\varphi }(\Omega )$ process,
interpolating broken line
Received by editor(s):
November 5, 2007
Published electronically:
December 29, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
