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Teoriya Veroyatnostei i ee Primeneniya, 1997, Volume 42, Issue 1, Pages 85–107
DOI: https://doi.org/10.4213/tvp1714 (Mi tvp1714) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Weak convergence of distributions of separable statistics

È. M. Kudlaev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (1484 kB) Citations (4)
DOI: https://doi.org/10.4213/tvp1714
Abstract: This paper focuses on weak limits (as the number of summands grows) of distributions of separable statistics taking values in locally compact Hausdorff Abelian groups. We consider a general method of deriving limit theorems for separable statistics that is applicable to any schemes. The weak limits under study are expressed in terms of the limit conditional distribution of an additive form associated with the separable statistic and determined from the independent random variables.
Received: 11.09.1996
English version:
Theory of Probability and its Applications, 1998, Volume 42, Issue 1, Pages 130–148
DOI: https://doi.org/10.1137/S0040585X97975952
Bibliographic databases:
Language: Russian
Citation: È. M. Kudlaev, “Weak convergence of distributions of separable statistics”, Teor. Veroyatnost. i Primenen., 42:1 (1997), 85–107; Theory Probab. Appl., 42:1 (1998), 130–148
Citation in format AMSBIB
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\by \`E.~M.~Kudlaev
\paper Weak convergence of distributions of separable statistics
\jour Teor. Veroyatnost. i Primenen.
\yr 1997
\vol 42
\issue 1
\pages 85--107
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1453332}
\zmath{https://zbmath.org/?q=an:0915.60035}
\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 1
\pages 130--148
\crossref{https://doi.org/10.1137/S0040585X97975952}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000073918900011}
Linking options:
  • https://www.mathnet.ru/eng/tvp1714
  • https://doi.org/10.4213/tvp1714
  • https://www.mathnet.ru/eng/tvp/v42/i1/p85
    • This publication is cited in the following 4 articles:
    1. E. M. Kudlaev, “Representation of the Characteristic Function for a Sum of a Random Number of Random Summands with Values in an LCA-Group*”, J Math Sci, 196:1 (2014), 50  crossref
    2. S. A. Maslenkov, “Decomposable Statistics and Random Placement of Particles over a Countable Set of Cells*”, J Math Sci, 189:6 (2013), 950  crossref
    3. E. M. Kudlaev, “On Finite-Dimensional Distributions of a Random Element Conditioned by the Sum of Random Elements*”, J Math Sci, 191:4 (2013), 588  crossref
    4. E. M. Kudlaev, “On conditions of existence of sums of functions of conditioned random elements”, J Math Sci, 127:4 (2005), 2099  crossref
    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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