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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
\mathnet{http://mi.mathnet.ru//eng/sm2908}
\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}
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  • https://doi.org/10.1070/SM1976v030n03ABEH002280
  • https://www.mathnet.ru/eng/sm/v143/i3/p416
  • This publication is cited in the following 87 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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