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Yurinskii, V. V.

Exponential inequalities for sums of random vectors. (English) Zbl 0346.60001

J. multivariate Analysis 6, 473-499 (1976).
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Cited in 2 Reviews
Cited in 71 Documents

MSC:

60A05 Axioms; other general questions in probability
62E99 Statistical distribution theory
62H99 Multivariate analysis
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References:

[1] Bernstein, S. N., (Gostechizdat, M.-L, Probability Theory (1946)), (in Russian)
[2] Borovkov, A. A., Boundary problems for random walk and large deviations in function spaces, Teor. Veroyatn. i Primen., XII, 4, 635-654 (1967), (in Russian)
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[8] Zolotarev, V. M., On a probabilistic problem, Teor. Veroyatn. i Primen., VI, 219-222 (1961), (in Russian)
[9] Zolotarev, V. M., Some remarks on multidimensional inequalities of Bernstein-Kolmogorov’s type, Teor. Veroyatn. i primen., XIII, 289-294 (1968), (in Russian) · Zbl 0169.21002
[10] Mogulskii, A. A., Large deviations in the space \(C(0, 1)\) for sums defined on a finite Markov chain, Sibirsk. Mat. Zh., XV, 61-75 (1974), (in Russian)
[11] Nagaev, S. V.; Fouk, D. H., Probability inequalities for sums of independent random variables, Teor. Veroyatn. i Primen., XVI, 660-675 (1971), (in Russian) · Zbl 0259.60024
[12] Prokhorov, A. V., On multidimensional analogues of S. N. Bernstein’s inequalities, Teor. Veroyatn. i Primen., XIII, 275-288 (1968), (in Russian) · Zbl 0169.20904
[13] Prokhorov, A. V., On a probability inequality, Mat. Zamyetki, 3, 737-744 (1968), (in Russian)
[14] Prokhorov, A. V., S. N. Bernstein’s inequalities in the multidimensional case, Teor. Veroyatn. i Primen., XIII, 462-470 (1968), (in Russian) · Zbl 0169.21001
[15] Prokhorov, A. V., Inequalities for Bessel functions of purely imaginary argument, Teor. Veroyatn. i Primen., XIII, 525-531 (1968), (in Russian) · Zbl 0167.46901
[16] Prokhorov, A. V., On sums of random vectors, Teor. Veroyatn. i Primen., XVIII, 193-195 (1973), (in Russian) · Zbl 0292.60080
[17] Prokhorov, Yu. V., An extension of S. N. Bernstein’s inequalities to the multidimensional case, Teor. Veroyatn. i Primen., XIII, 266-274 (1968), (in Russian) · Zbl 0165.20301
[18] Sudakov, V. N.; Tzirelson, B. S., Extremal properties of half-spaces for spherically invariant measures, Zap. Nauchn. Seminarov Lomi, 41, 14-24 (1974), (in Russian) · Zbl 0351.28015
[19] Freidlin, M. I., Functional of action for a class of random processes, Teor. Veroyatn. i Primen., XVII, 536-541 (1972), (in Russian) · Zbl 0268.60040
[20] Ebralidze, Sh. S., Inequalities for large deviation probabilities in the multidimensional case, Teor. Veroyatn. i Primen., XVI, 755-759 (1971), (in Russian)
[21] Yurinskiĭ, V. V., On an infinite-dimensional variant of S. N. Bernstein’s inequalities, Teor. Veroyatn. i Primen., XV, 106-107 (1970), (in Russian) · Zbl 0193.44703
[22] Yurinskiĭ, V. V., On inequalities for large deviations of certain statistics, Teor. Veroyatn. i Primen., XVI, 386-389 (1971), (in Russian) · Zbl 0266.60003
[23] Yurinskiĭ, V. V., Exponential inequalities for large deviations, Teor. Veroyatn. i Primen., XIX, 152-153 (1974), (in Russian)
[24] Yurinskiĭ, V. V., Exponential bounds for smooth fields, Teor. Veroyatn. i Primen., XIX, 230-235 (1974), (in Russian)
[25] Berman, S. M., Maxima and high level excursions of stationary Gaussian processes, Trans. Amer. Math. Soc., 160, 65-86 (1971) · Zbl 0228.60014
[26] Fernique, X., Integrabilité des vecteurs Gaussiens, C. R. Acad. Sci. Paris Ser. A, 270, 1698-1699 (1970) · Zbl 0206.19002
[27] Fernique, X., Regularité de processus Gaussiens, Inventions Math., 12, 304-320 (1971) · Zbl 0217.21104
[28] Fortet, R.; Mourier, E., Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math., XV, 62-79 (1955) · Zbl 0068.11104
[29] Hoeffding, W., Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58, 13-30 (1963) · Zbl 0127.10602
[30] Kahane, J.-P, Sur les sommes vectorielles, C. R. Acad. Sci. Paris., 259, 2577-2580 (1964) · Zbl 0127.35504
[31] Landau, H. J.; Shepp, L. A., On the supremum of a Gaussian process, Sankhya Ser. A., 32, 369-379 (1970) · Zbl 0218.60039
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