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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 3, Pages 638–645
(Mi tvp4000)
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This article is cited in 7 scientific papers (total in 7 papers)
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.
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
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https://www.mathnet.ru/eng/tvp4000 https://www.mathnet.ru/eng/tvp/v38/i3/p638
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Abstract page: | 152 | Full-text PDF : | 64 | First page: | 11 |
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