000 | 03685nam a22004815i 4500 | ||
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001 | 978-3-540-48111-9 | ||
003 | DE-He213 | ||
005 | 20190213151153.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1993 gw | s |||| 0|eng d | ||
020 |
_a9783540481119 _9978-3-540-48111-9 |
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024 | 7 |
_a10.1007/BFb0073527 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBT _2bicssc |
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_aMAT029000 _2bisacsh |
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_aPBT _2thema |
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_aPBWL _2thema |
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082 | 0 | 4 |
_a519.2 _223 |
100 | 1 |
_aMolchanov, Ilya S. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aLimit Theorems for Unions of Random Closed Sets _h[electronic resource] / _cby Ilya S. Molchanov. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1993. |
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300 |
_aX, 158 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1561 |
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505 | 0 | _aDistributions of random closed sets -- Survey on stability of random sets and limit theorems for Minkowski addition -- Infinite divisibility and stability of random sets with respect to unions -- Limit theorems for normalized unions of random closed sets -- Almost sure convergence of unions of random closed sets -- Multivalued regularly varying functions and their applications to limit theorems for unions of random sets -- Probability metrics in the space of random sets distributions -- Applications of limit theorems. | |
520 | _aThe book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed. | ||
650 | 0 | _aDistribution (Probability theory. | |
650 | 1 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662165720 |
776 | 0 | 8 |
_iPrinted edition: _z9783540573937 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1561 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0073527 |
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912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
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