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

This article is cited in 18 scientific papers (total in 18 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)
References: PDF file   HTML file

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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    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. Tran Loc Hung, Phan Tri Kien, “On the Rates of Convergence in Weak Limit Theorems For Geometric Random Sums of the Strictly Stationary Sequence of M-Dependent Random Variables”, Lith. Math. J.  crossref  mathscinet  isi
    2. Hung T.L., Kien Ph.T., “On the Order of Approximation in Limit Theorems For Negative-Binomial Sums of Strictly Stationary M-Dependent Random Variables”, Acta Math. Vietnam  crossref  mathscinet  isi
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. Bobkov S.G., “Central Limit Theorem and Diophantine Approximations”, J. Theor. Probab., 31:4 (2018), 2390–2411  crossref  mathscinet  zmath  isi  scopus
    9. S. G. Bobkov, “Khinchine's theorem and edgeworth approximations for weighted sums”, Ann. Stat., 47:3 (2019), 1616–1633  crossref  mathscinet  isi
    10. Tran Loc Hung, Phan Tri Kien, “On the rates of convergence to symmetric stable laws for distributions of normalized geometric random sums”, Filomat, 33:10 (2019), 3073–3084  crossref  isi
    11. Tran Loc Hung, Phan Tri Kien, Nguyen Tan Nhut, “On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums”, Kybernetika, 55:6 (2019), 961–975  crossref  isi
    12. A. Dytso, H. V. Poor, “On stability of linear estimators in Poisson noise”, Conference Record of the 2019 Fifty-Third Asilomar Conference on Signals, Systems & Computers, Conference Record of the Asilomar Conference on Signals Systems and Computers, ed. M. Matthews, IEEE, 2019, 670–674  isi
    13. Tran Loc Hung, Phan Tri Kien, “On the rates of convergence in weak limit theorems for normalized geometric sums”, Bull. Korean. Math. Soc., 57:5 (2020), 1115–1126  crossref  mathscinet  zmath  isi
    14. A. Dytso, H. V. Poor, “Estimation in Poisson noise: properties of the conditional mean estimator”, IEEE Trans. Inf. Theory, 66:7 (2020), 4304–4323  crossref  mathscinet  zmath  isi
    15. S. G. Bobkov, M. Ledoux, “Transport inequalities on euclidean spaces for non-euclidean metrics”, J. Fourier Anal. Appl., 26:4 (2020), 60  crossref  mathscinet  zmath  isi
    16. S. G. Bobkov, “Edgeworth corrections in randomized central limit theorems”, Geometric Aspects of Functional Analysis: Israel Seminar (Gafa) 2017-2019, Vol i, Lect. Notes Math., Lecture Notes in Mathematics, 2256, eds. B. Klartag, E. Milman, Springer, 2020, 71–97  crossref  mathscinet  isi
    17. P. Cattiaux, A. Guillin, “On the Poincare constant of log-concave measures”, Geometric Aspects of Functional Analysis: Israel Seminar (Gafa) 2017-2019, Vol i, Lect. Notes Math., Lecture Notes in Mathematics, 2256, eds. B. Klartag, E. Milman, Springer, 2020, 171–217  crossref  mathscinet  isi
    18. S. G. Bobkov, G. P. Chistyakov, F. Goetze, “Poincare inequalities and normal approximation for weighted sums”, Electron. J. Probab., 25 (2020), 155  crossref  mathscinet  isi
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