V. V. Yurinskii, “On an infinite-dimensional version of S. N. Bernstein's inequalities”, Teor. Veroyatnost. i Primenen., 15:1 (1970), 106–107; Theory Probab. Appl., 15:1 (1970), 108

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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 1, Pages 106–107 (Mi tvp1567)

This article is cited in 19 scientific papers (total in 19 papers)

Short Communications

On an infinite-dimensional version of S. N. Bernstein's inequalities

V. V. Yurinskii

Moscow

Full-text PDF (131 kB) Citations (19)

Abstract: Probability inequalities for sums of bounded independent random vectors in a Hilbert space are obtained. Reduction to one-ditnensieeal case yields a considerable simplification of the proofs.

Received: 17.09.1969

English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 1, Pages 108–109
DOI: https://doi.org/10.1137/1115008

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Yurinskii, “On an infinite-dimensional version of S. N. Bernstein's inequalities”, Teor. Veroyatnost. i Primenen., 15:1 (1970), 106–107; Theory Probab. Appl., 15:1 (1970), 108–109

Citation in format AMSBIB

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\pages 106--107

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\transl

\jour Theory Probab. Appl.

\yr 1970

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\pages 108--109

\crossref{https://doi.org/10.1137/1115008}

Linking options:

https://www.mathnet.ru/eng/tvp1567

https://www.mathnet.ru/eng/tvp/v15/i1/p106

This publication is cited in the following 19 articles:

Emanuele Dolera, Stefano Favaro, Edoardo Mainini, “Strong posterior contraction rates via Wasserstein dynamics”, Probab. Theory Relat. Fields, 2024
Vivien Cabannes, 2023 IEEE International Conference on Big Data (BigData), 2023, 1059
Vladislav Kargin, “A large deviation inequality for vector functions on finite reversible Markov Chains”, Ann. Appl. Probab., 17:4 (2007)
F. Götze, Yu. V. Prokhorov, V. V. Ulyanov, “Bounds for characteristic functions of polynomials in asymptotically normal random variables”, Russian Math. Surveys, 51:2 (1996), 181–204
E. R. Vvedenskaya, “On the Monotonity of Exact Upper Sequences for Sums of Independent Random Vectors in Hilbert Space”, Theory Probab. Appl., 33:1 (1988), 148–151
I. F. Pinelis, A. I. Sahanenko, “Remarks on inequalities for the probabilities of large deviations”, Theory Probab. Appl., 30:1 (1986), 143–148
E. R. Vvedenskaya, “On asymptotic behaviour of sums of random vectors with values in Hilbert space”, Theory Probab. Appl., 29:3 (1985), 620–622
L. V. Osipov, V. I. Rotar', “On an infinite-dimensional central limit theorem”, Theory Probab. Appl., 29:2 (1985), 375–383
Yu. V. Borovskih, “Estimates of the characteristic functions with applications to $\omega^2$ -statistics. I”, Theory Probab. Appl., 29:3 (1985), 488–503
B. A. Zalesskiǐ, “Estimates of the accuracy of normal approximation in a Hilbert space”, Theory Probab. Appl., 27:2 (1983), 290–298
V. M. Kruglov, S. N. Antonov, “On the asymptotical behaviour of infinitely divisible distributions in a Banach space”, Theory Probab. Appl., 27:4 (1983), 667–687
L. V. Osipov, “On the probabilities of large deviations for sums of independent random vectors”, Theory Probab. Appl., 23:3 (1979), 490–506
N. К. Arenbaev, “On inequalities for random vectors”, Theory Probab. Appl., 22:3 (1978), 574–579
V. V. Yurinskiǐ, “On the error of the Gaussian approximation for convolutions”, Theory Probab. Appl., 22:2 (1978), 236–247
“Summaries of papers presented at the sessions of the probability and statistics section of the Moscow mathematical society (February–October 1974)”, Theory Probab. Appl., 20:2 (1976), 428–443
V. V. Yurinskii, “Exponential bounds for large deviations”, Theory Probab. Appl., 19:1 (1974), 154–155
V. M. Kruglov, “Convergence of numerical characteristics of sums of independent random variables with vakues in a Hilbert space”, Theory Probab. Appl., 18:4 (1974), 694–712
V. V. Yurinskiǐ, “On inequalities for large deviations of certain statistics”, Theory Probab. Appl., 16:2 (1971), 385–387
Š. S. Èbralidze, “Inequalities for the probabilities of large deviations in the multi-dimensional case”, Theory Probab. Appl., 16:4 (1971), 733–737

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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