The Banach spaces $\mathbf {F}_\psi (\Omega )$ of random variables
Authors:
Yu. V. Kozachenko and Yu. Yu. Mlavets$’$
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 86 (2013), 105-121
MSC (2010):
Primary 60G07; Secondary 65C05
DOI:
https://doi.org/10.1090/S0094-9000-2013-00892-8
Published electronically:
August 20, 2013
MathSciNet review:
2986453
Full-text PDF Free Access
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Additional Information
Abstract: Some properties of random variables and stochastic processes belonging to the spaces $\mathbf {F}_\psi (\Omega )$ are studied.
References
- Yu. V. Kozachenko and Yu. Yu. Mlavets, Probability of large deviations of sums of random processes from Orlicz space, Monte Carlo Methods Appl. 17 (2011), no. 2, 155–168. MR 2819705, DOI https://doi.org/10.1515/MCMA.2011.007
- O. Kurbanmuradov and K. Sabelfeld, Exponential bounds for the probability deviations of sums of random fields, Monte Carlo Methods Appl. 12 (2006), no. 3-4, 211–229. MR 2274693, DOI https://doi.org/10.1163/156939606778705218
- S. V. Ermakov and E. I. Ostrovskiĭ, Conditions for the continuity, exponential bounds, and central limit theorem for random fields, Dep. VINITI no. 3752-B.86.0., 1986. (Russian)
- 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
- E. A. Abzhanov and Yu. V. Kozachenko, Some properties of random processes in Banach $K_\sigma $-spaces, Ukrain. Mat. Zh. 37 (1985), no. 3, 275–280, 403 (Russian). MR 795565
- 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
References
- Yu. V. Kozachenko and Yu. Yu. Mlavets, Probability of large deviations of sums of random processes from Orlicz space, Monte Carlo Methods Appl. 17 (2011), no. 17, 155–168. MR 2819705 (2012e:65009)
- O. Kurbanmuradov and K. Sabelfeld, Exponential bounds for the probability deviations of sums of random fields, Monte Carlo Methods Appl. 12 (2006), no. 3–4, 211–229. MR 2274693 (2008a:60132)
- S. V. Ermakov and E. I. Ostrovskiĭ, Conditions for the continuity, exponential bounds, and central limit theorem for random fields, Dep. VINITI no. 3752-B.86.0., 1986. (Russian)
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
- E. A. Abzhanov and Yu. V. Kozachenko, Some properties of random processes in Banach $K_\sigma$-spaces, Ukrain. Math. J. 37 (1985), no. 3, 275–280. MR 795565 (87m:60095)
- Yu. V. Kozachenko and E. I. Ostrovskiĭ, Banach spaces of random variables of subgaussian type, Theory Probab. Math. Statist. 32 (1985), 45–56. MR 0882158 (88e:60009)
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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, 4E, Kiev 03127, Ukraine
Email:
ykoz@ukr.net
Yu. Yu. Mlavets$’$
Affiliation:
Department of Cybernetics and Applied Mathematics, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod 88000, Ukraine
Email:
yura-mlavec@ukr.net
Keywords:
Orlicz spaces,
Banach spaces of random variables,
stochastic processes,
moment norms
Received by editor(s):
November 17, 2011
Published electronically:
August 20, 2013
Article copyright:
© Copyright 2013
American Mathematical Society
