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

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.

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

Bibliographic databases:

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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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
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