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 Uspekhi Mat. Nauk, 2016, Volume 71, Issue 6(432), Pages 37–98 (Mi umn9749)

Proximity of probability distributions in terms of Fourier–Stieltjes transforms

S. G. Bobkov

School of Mathematics, University of Minnesota, Minneapolis, MN, USA

Abstract: A survey is given of some results on smoothing inequalities for various probability metrics (in particular, for the Kolmogorov distance), and some analogues of these results in the class of functions of bounded variation are presented.
Bibliography: 61 titles.

Keywords: probability metrics, smoothing inequalities.

 Funding Agency Grant Number National Science Foundation NSF DMS-1612961 Alexander von Humboldt-Stiftung This work was carried out with the support of the Alexander von Humboldt Foundation and the National Science Foundation (grant NSF DMS-1612961).

DOI: https://doi.org/10.4213/rm9749

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English version:
Russian Mathematical Surveys, 2016, 71:6, 1021–1079

Bibliographic databases:

UDC: 517.984+512.77
MSC: Primary 60E05, 60E10; Secondary 60B10, 60F05
Revised: 11.07.2016

Citation: S. G. Bobkov, “Proximity of probability distributions in terms of Fourier–Stieltjes transforms”, Uspekhi Mat. Nauk, 71:6(432) (2016), 37–98; Russian Math. Surveys, 71:6 (2016), 1021–1079

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/umn9749
• https://doi.org/10.4213/rm9749
• http://mi.mathnet.ru/eng/umn/v71/i6/p37

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

This publication is cited in the following articles:
1. S. G. Bobkov, “Asymptotic expansions for products of characteristic functions under moment assumptions of non-integer orders”, Convexity and concentration, IMA Volumes in Mathematics and Its Applications, 161, Springer, New York, NY, 2017, 297–357
2. I. Shevtsova, “On the absolute constants in Nagaev-Bikelis-type inequalities”, Inequalities and extremal problems in probability and statistics, Selected topics, ed. Pinelis I., Academic Press, London, 2017, 47–102
3. I. G. Shevtsova, “Convergence rate estimates in the global CLT for compound mixed Poisson distributions”, Theory Probab. Appl., 63:1 (2018), 72–93
4. S. G. Bobkov, “Berry-Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances”, Probab. Theory Related Fields, 170:1-2 (2018), 229–262
5. S. G. Bobkov, G. P. Chistyakov, F. Götze, “Berry-Esseen bounds for typical weighted sums”, Electron. J. Probab., 23 (2018), 92, 22 pp.
6. Bobkov S.G., “Khinchine'S Theorem and Edgeworth Approximations For Weighted Sums”, Ann. Stat., 47:3 (2019), 1616–1633
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