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

This article is cited in 6 scientific papers (total in 6 papers)

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

Full text: PDF file (910 kB)
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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
Received: 30.12.2015
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/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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  isi
    3. I. G. Shevtsova, “Convergence rate estimates in the global CLT for compound mixed Poisson distributions”, Theory Probab. Appl., 63:1 (2018), 72–93  mathnet  crossref  crossref  isi  elib
    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  crossref  mathscinet  zmath  isi  scopus
    5. S. G. Bobkov, G. P. Chistyakov, F. Götze, “Berry-Esseen bounds for typical weighted sums”, Electron. J. Probab., 23 (2018), 92, 22 pp.  crossref  mathscinet  zmath  isi  scopus
    6. Bobkov S.G., “Khinchine'S Theorem and Edgeworth Approximations For Weighted Sums”, Ann. Stat., 47:3 (2019), 1616–1633  crossref  mathscinet  isi
  • Успехи математических наук Russian Mathematical Surveys
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