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Teor. Veroyatnost. i Primenen., 1993, Volume 38, Issue 3, Pages 638–645 (Mi tvp4000)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Limit theorems for unions of random sets under multiplicative normalization

I. S. Molchanov

Kiev Technological Institute of the Food Industry

Abstract: This paper finds conditions for weak convergence of normalized unions $a_n^{ - 1} (A_1 \cup \ldots A_n )$ of independent and identically distributed random closed sets $A_1 , \ldots ,A_n$ in terms of regular variation of corresponding accompanying functionals. The special case $A_1 = M(\xi )$, where $M$ is a multivalued function and $\xi $ a random vector with regularly varying density is also considered.

Keywords: random closed sets, regularly varying function, capacity, max-stable law.

Full text: PDF file (1575 kB)

English version:
Theory of Probability and its Applications, 1993, 38:3, 541–547

Bibliographic databases:

Received: 20.07.1990

Citation: I. S. Molchanov, “Limit theorems for unions of random sets under multiplicative normalization”, Teor. Veroyatnost. i Primenen., 38:3 (1993), 638–645; Theory Probab. Appl., 38:3 (1993), 541–547

Citation in format AMSBIB
\Bibitem{Mol93}
\by I.~S.~Molchanov
\paper Limit theorems for unions of random sets under multiplicative normalization
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 3
\pages 638--645
\mathnet{http://mi.mathnet.ru/tvp4000}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1404672}
\zmath{https://zbmath.org/?q=an:0807.60015}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 3
\pages 541--547
\crossref{https://doi.org/10.1137/1138054}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Molchanov I., Theory of Random Sets, 2Nd Edition, Probability Theory and Stochastic Modelling, 87, Springer International Publishing Ag, 2017  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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