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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 2, Pages 264–287 (Mi tvp2295)  

This article is cited in 131 scientific papers (total in 132 papers)

Probability metrics

V. M. Zolotarev

Moscow
Abstract: We review some notions and results of the theory of probability metrics. During the last few years this new branch of the probability theory was developing intensively both in our country and abroad. The review is not complete because of the limitation of the size of the paper. To some extent this defect is compensated by the list of references.
Received: 25.01.1983
English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 1, Pages 278–302
DOI: https://doi.org/10.1137/1128025
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Zolotarev, “Probability metrics”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 264–287; Theory Probab. Appl., 28:1 (1984), 278–302
Citation in format AMSBIB
\Bibitem{Zol83}
\by V.~M.~Zolotarev
\paper Probability metrics
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 2
\pages 264--287
\mathnet{http://mi.mathnet.ru/tvp2295}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=700210}
\zmath{https://zbmath.org/?q=an:0533.60025|0514.60026}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 1
\pages 278--302
\crossref{https://doi.org/10.1137/1128025}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SS85900005}
Linking options:
  • https://www.mathnet.ru/eng/tvp2295
  • https://www.mathnet.ru/eng/tvp/v28/i2/p264
    Erratum
    This publication is cited in the following 132 articles:
    1. Sreejith Sreekumar, Ziv Goldfeld, Kengo Kato, “Limit Distribution Theory for f-Divergences”, IEEE Trans. Inform. Theory, 70:2 (2024), 1233  crossref
    2. M. P. Savelov, “Two-sided estimates for the sum of probabilities of errors in the multiple hypotheses testing problem with finite number of hypotheses about a nonhomogeneous sample”, Theory Probab. Appl., 69:2 (2024), 322–330  mathnet  crossref  crossref
    3. W. Römisch, T. M. Surowiec, “Asymptotic properties of Monte Carlo methods in elliptic PDE-constrained optimization under uncertainty”, Numer. Math., 2024  crossref
    4. Euijoon Kwon, Jong-Min Park, Jae Sung Lee, Yongjoo Baek, “Unified hierarchical relationship between thermodynamic tradeoff relations”, Phys. Rev. E, 110:4 (2024)  crossref
    5. Marieke Stolte, Franziska Kappenberg, Jörg Rahnenführer, Andrea Bommert, “Methods for quantifying dataset similarity: a review, taxonomy and comparison”, Statist. Surv., 18:none (2024)  crossref
    6. Jiequn Han, Ruimeng Hu, Jihao Long, “A class of dimension-free metrics for the convergence of empirical measures”, Stochastic Processes and their Applications, 164 (2023), 242  crossref
    7. Ioannis Kyriakou, Riccardo Brignone, Gianluca Fusai, “Unified Moment-Based Modeling of Integrated Stochastic Processes”, Operations Research, 2023  crossref
    8. Aravind Gollakota, Adam R. Klivans, Pravesh K. Kothari, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 2023, 1657  crossref
    9. Tasos C. Christofides, Charalambos Charalambous, “Asymptotic normality of U-statistics based on i.i.d. or negatively associated observations by utilizing Zolotarev's ideal metric”, Communications in Statistics - Theory and Methods, 52:12 (2023), 4083  crossref
    10. Tianle Liu, Morgane Austern, “Wasserstein-p bounds in the central limit theorem under local dependence”, Electron. J. Probab., 28:none (2023)  crossref
    11. Vladimir Makarenko, Irina Shevtsova, “Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions”, Mathematics, 11:3 (2023), 625  crossref
    12. Andreas Anastasiou, Alessandro Barp, François-Xavier Briol, Bruno Ebner, Robert E. Gaunt, Fatemeh Ghaderinezhad, Jackson Gorham, Arthur Gretton, Christophe Ley, Qiang Liu, Lester Mackey, Chris J. Oates, Gesine Reinert, Yvik Swan, “Stein's Method Meets Computational Statistics: A Review of Some Recent Developments”, Statist. Sci., 38:1 (2023)  crossref
    13. Eric Beutner, Henryk Zähle, “Donsker results for the empirical process indexed by functions of locally bounded variation and applications to the smoothed empirical process”, Bernoulli, 29:1 (2023)  crossref
    14. 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  mathnet  crossref  crossref  mathscinet  zmath
    15. Omar Besbes, Will Ma, Omar Mouchtaki, “Beyond IID: Data-Driven Decision-Making in Heterogeneous Environments”, SSRN Journal, 2022  crossref
    16. Henryk Zähle, “A concept of copula robustness and its applications in quantitative risk management”, Finance Stoch, 26:4 (2022), 825  crossref
    17. 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, 46:1 (2021), 203–224  crossref  isi
    18. M. Hoffhues, W. Römisch, T. M. Surowiec, “On quantitative stability in infinite-dimensional optimization under uncertainty”, Optim Lett, 15:8 (2021), 2733  crossref
    19. “In memory of V. M. Zolotarev (02.27.1931–11.07.2019)”, Theory Probab. Appl., 65:1 (2020), 175–178  mathnet  crossref  crossref  isi
    20. Zeifman A. Korolev V. Satin Ya., “Two Approaches to the Construction of Perturbation Bounds For Continuous-Time Markov Chains”, Mathematics, 8:2 (2020), 253  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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