A. Yu. Zaǐcev, T. V. Arak, “On the rate of convergence in the second Kolmogorov's uniform limit theorem”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 333–353; Theory Probab. Appl., 28:2 (1984), 351

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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 2, Pages 333–353 (Mi tvp2298)

This article is cited in 12 scientific papers (total in 12 papers)

On the rate of convergence in the second Kolmogorov's uniform limit theorem

A. Yu. Zaĭcev^a, T. V. Arak^b

^a Leningrad
^b Tallinn

Full-text PDF (2893 kB) Citations (12)

Abstract: In this paper we study the accuracy of infinitely divisible approximation for the distributions of sums of independent random variables with arbitrary distributions. This problem was stated by A. N. Kolmogorov. Some unimprovable estimates are obtained.

Received: 10.01.1983

English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 2, Pages 351–374
DOI: https://doi.org/10.1137/1128028

Bibliographic databases:

Language: Russian

Citation: A. Yu. Zaǐcev, T. V. Arak, “On the rate of convergence in the second Kolmogorov's uniform limit theorem”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 333–353; Theory Probab. Appl., 28:2 (1984), 351–374

Citation in format AMSBIB

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\pages 333--353

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\transl

\jour Theory Probab. Appl.

\yr 1984

\vol 28

\issue 2

\pages 351--374

\crossref{https://doi.org/10.1137/1128028}

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Linking options:

https://www.mathnet.ru/eng/tvp2298

https://www.mathnet.ru/eng/tvp/v28/i2/p333

Erratum

Letter to the editors
A. Yu. Zaitsev
Teor. Veroyatnost. i Primenen., 1984, 29:1, 201

This publication is cited in the following 12 articles:

F. Götze, A. Yu. Zaitsev, “On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem”, Theory Probab. Appl., 67:1 (2022), 1–16
V. Čekanavičius, S. Y. Novak, “Compound Poisson approximation”, Probab. Surveys, 19:none (2022)
F. Gettse, A. Yu. Zaitsev, D. N. Zaporozhets, “Uluchshennyi mnogomernyi variant vtoroi ravnomernoi predelnoi teoremy Kolmogorova”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 71–85
Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “Toward the History of the Saint Petersburg School of Probability and Statistics. i. Limit Theorems For Sums of Independent Random Variables”, Vestnik St. Petersburg Univ. Math., 51:2 (2018), 144–163
F. Götze, Yu. S. Eliseeva, A. Yu. Zaitsev, “Arak inequalities for concentration functions and the Littlewood–Offord problem”, Theory Probab. Appl., 62:2 (2018), 196–215
Theory Probab. Appl., 59:2 (2015), 222–243
A. Yu. Zaitsev, “On the approximation of convolutions by accompanying laws in the scheme of series”, J. Math. Sci. (N. Y.), 199:2 (2014), 162–167
A. Yu. Zaitsev, “Multidimensional version of the second uniform limit theorem of Kolmogorov”, Theory Probab. Appl., 34:1 (1989), 108–128
A. Yu. Zaitsev, “On the Uniform Approximation of Distributions of Sums of Independent Random Variables”, Theory Probab. Appl., 32:1 (1987), 40–47
A. Yu. Zaitsev, “Letter to the editors”, Theory Probab. Appl., 29:1 (1985), 199–199
E. L. Presman, “On the approximation of binomial distributions by means oi infinitely divisible ones”, Theory Probab. Appl., 28:2 (1984), 393–403
A. Yu. Zaitsev, “On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws”, Theory Probab. Appl., 28:4 (1984), 657–669

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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