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Mathematics of the USSR-Sbornik, 1976, Volume 30, Issue 3, Pages 373–401
DOI: https://doi.org/10.1070/SM1976v030n03ABEH002280
(Mi sm2908)
 

This article is cited in 87 scientific papers (total in 87 papers)

Metric distances in spaces of random variables and their distributions

V. M. Zolotarev
References:
Abstract: In this paper the concept of a metric in the space of random variables defined on a probability space is introduced. The principle of three stages in the study of approximation problems is formulated, in particular problems of approximating distributions.
Various facts connected with the use of metrics in these three stages are presented and proved. In the second part of the paper a series of results is introduced which are related to stability problems in characterizing distributions and to problems of estimating the remainder terms in limiting approximations of distributions of sums of independent random variables.
Both the account of properties of metrics and the application of these facts in the second part of the paper are presented under the assumption that the random variables take values in a general space (metric, Banach or Hilbert space).
Bibliography: 11 titles.
Received: 19.04.1976
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: Primary 60E05, 60F05; Secondary 54E35
Language: English
Original paper language: Russian
Citation: V. M. Zolotarev, “Metric distances in spaces of random variables and their distributions”, Math. USSR-Sb., 30:3 (1976), 373–401
Citation in format AMSBIB
\Bibitem{Zol76}
\by V.~M.~Zolotarev
\paper Metric distances in spaces of random variables and their distributions
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 3
\pages 373--401
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\crossref{https://doi.org/10.1070/SM1976v030n03ABEH002280}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=467869}
\zmath{https://zbmath.org/?q=an:0367.60003}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976FN58700007}
Linking options:
  • https://www.mathnet.ru/eng/sm2908
  • https://doi.org/10.1070/SM1976v030n03ABEH002280
  • https://www.mathnet.ru/eng/sm/v143/i3/p416
  • This publication is cited in the following 87 articles:
    1. Lutz Mattner, “A convolution inequality, yielding a sharper Berry–Esseen theorem for summands Zolotarev-close to normal”, Theor. Probability and Math. Statist., 2024  crossref
    2. Marieke Stolte, Franziska Kappenberg, Jörg Rahnenführer, Andrea Bommert, “Methods for quantifying dataset similarity: a review, taxonomy and comparison”, Statist. Surv., 18:none (2024)  crossref
    3. Feng Liu, Zhi Chen, Shuming Wang, “Globalized Distributionally Robust Counterpart”, INFORMS Journal on Computing, 35:5 (2023), 1120  crossref
    4. Lorenzo Pareschi, Giuseppe Toscani, “The Kinetic Theory of Mutation Rates”, Axioms, 12:3 (2023), 265  crossref
    5. Alexander Vidal, Samy Wu Fung, Luis Tenorio, Stanley Osher, Levon Nurbekyan, “Taming hyperparameter tuning in continuous normalizing flows using the JKO scheme”, Sci Rep, 13:1 (2023)  crossref
    6. Anna Gusakova, Matthias Reitzner, Christoph Thäle, “Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon”, Annales Henri Lebesgue, 6 (2023), 875  crossref
    7. Florian Heinemann, Axel Munk, Yoav Zemel, “Randomized Wasserstein Barycenter Computation: Resampling with Statistical Guarantees”, SIAM Journal on Mathematics of Data Science, 4:1 (2022), 229  crossref
    8. Marcel Klatt, Axel Munk, Yoav Zemel, “Limit laws for empirical optimal solutions in random linear programs”, Ann Oper Res, 315:1 (2022), 251  crossref
    9. Anil Aswani, Matt Olfat, “Optimization hierarchy for fair statistical decision problems”, Ann. Statist., 50:6 (2022)  crossref
    10. Giuseppe Toscani, “On Fourier-Based Inequality Indices”, Entropy, 24:10 (2022), 1393  crossref
    11. Werner Zellinger, Bernhard A. Moser, Susanne Saminger-Platz, “On generalization in moment-based domain adaptation”, Ann Math Artif Intell, 89:3-4 (2021), 333  crossref
    12. Werner Zellinger, Bernhard A. Moser, “On the truncated Hausdorff moment problem under Sobolev regularity conditions”, Applied Mathematics and Computation, 400 (2021), 126057  crossref
    13. Philippe Briand, Christel Geiss, Stefan Geiss, Céline Labart, “Donsker-type theorem for BSDEs: Rate of convergence”, Bernoulli, 27:2 (2021)  crossref
    14. Tran Loc Hung, Phan TriKien, “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, 60:2 (2020), 173  crossref
    15. Andrey Borisov, Igor Sokolov, “Optimal Filtering of Markov Jump Processes Given Observations with State-Dependent Noises: Exact Solution and Stable Numerical Schemes”, Mathematics, 8:4 (2020), 506  crossref
    16. Pavel S. Ruzankin, Igor S. Borisov, “On the rate of Poisson approximation to Bernoulli partial sum processes”, Statistics & Probability Letters, 162 (2020), 108754  crossref
    17. Ralph Neininger, Henning Sulzbach, “On a functional contraction method”, Ann. Probab., 43:4 (2015)  crossref
    18. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi, The Methods of Distances in the Theory of Probability and Statistics, 2013, 335  crossref
    19. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi, The Methods of Distances in the Theory of Probability and Statistics, 2013, 67  crossref
    20. Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi, The Methods of Distances in the Theory of Probability and Statistics, 2013, 421  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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