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 Mat. Sb. (N.S.), 1976, Volume 101(143), Number 3(11), Pages 416–454 (Mi msb2908)

Metric distances in spaces of random variables and their distributions

V. M. Zolotarev

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.

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English version:
Mathematics of the USSR-Sbornik, 1976, 30:3, 373–401

Bibliographic databases:

UDC: 519.2
MSC: Primary 60E05, 60F05; Secondary 54E35

Citation: V. M. Zolotarev, “Metric distances in spaces of random variables and their distributions”, Mat. Sb. (N.S.), 101(143):3(11) (1976), 416–454; 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 Mat. Sb. (N.S.) \yr 1976 \vol 101(143) \issue 3(11) \pages 416--454 \mathnet{http://mi.mathnet.ru/msb2908} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=467869} \zmath{https://zbmath.org/?q=an:0367.60003} \transl \jour Math. USSR-Sb. \yr 1976 \vol 30 \issue 3 \pages 373--401 \crossref{https://doi.org/10.1070/SM1976v030n03ABEH002280} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FN58700007} 

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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:
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