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Theory of Probability and Mathematical Statistics

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The Banach spaces $ \mathbf{F}_\psi(\Omega)$ of random variables


Authors: Yu. V. Kozachenko and Yu. Yu. Mlavets$’$
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
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
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Abstract | References | Similar Articles | Additional Information

Abstract: Some properties of random variables and stochastic processes belonging to the spaces $ \mathbf {F}_\psi (\Omega )$ are studied.


References [Enhancements On Off] (What's this?)

  • 1. 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)
  • 2. 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)
  • 3. 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)
  • 4. 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)
  • 5. 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)
  • 6. 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

DOI: https://doi.org/10.1090/S0094-9000-2013-00892-8
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

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