Characterization of \(\gamma\)-subgaussian random elements in a Banach space. (English. Russian original) Zbl 1359.46009
J. Math. Sci., New York 216, No. 4, 564-568 (2016); translation from Sovrem. Mat. Prilozh. 94 (2014).
Summary: We give a characterization of weakly subgaussian random elements that are \(\gamma\)-subgaussian in infinite-dimensional Banach and Hilbert spaces.
MSC:
| 46B09 | Probabilistic methods in Banach space theory |
| 60B11 | Probability theory on linear topological spaces |
References:
| [1] | V. V. Buldygin and Yu. V. Kozachenko, “Sub-Gaussian random variables,” Ukr. Mat. Zh., 32, 723-730 (1980). · Zbl 0459.60002 · doi:10.1007/BF01087176 |
| [2] | V. V. Buldygin and Yu. V. Kozachenko, “Metric characteristics of random variables and processes,” in: Trans. Math. Monogr., 188, Am. Math. Soc., Providence, Rhode Island (2000). · Zbl 0998.60503 |
| [3] | R. Giuliano Antonini, “Sub-Gaussian random variables in Hilbert spaces,” Rend. Sem. Mat. Univ. Padova, 98, 89-99 (1997). · Zbl 0892.60049 |
| [4] | J. Hoffmann-Jørgensen and G. Pisier, “The law of large numbers and the central limit theorem in Banach spaces,” Ann. Probab., 4, No. 4, 587-599 (1976). · Zbl 0368.60022 · doi:10.1214/aop/1176996029 |
| [5] | J.-P. Kahane, “Propriétés locales des fonctions à séries de Fourier aléatoires,” Stud. Math., 19, 1-25 (1960). · Zbl 0096.11402 |
| [6] | M. Talagrand, “Regularity of Gaussian processes,” Acta Math., 159, Nos. 1-2, 99-149 (1987). · Zbl 0712.60044 |
| [7] | N. D. Tien, V. I. Tarieladze, and R. Vidal, “On summing and related operators acting from a Hilbert space,” Bull. Polish Acad. Sci. Math., 46, No. 4, 365-375 (1998). · Zbl 0918.60032 |
| [8] | N. N. Vakhania, V. V. Kvaratskhelia, and V. I. Tarieladze, “Weakly sub-Gaussian random elements in Banach spaces,” Ukr. Mat. Zh., 57, No. 9, 1187-1208 (2005). · Zbl 1093.60005 |
| [9] | N. N. Vakhania, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions on Banach Spaces, Math. Appl., Soviet Ser., 14, Dordrecht (1987). · Zbl 0698.60003 |
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