000 03685nam a22004815i 4500
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
024 7 _a10.1007/BFb0073527
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aMolchanov, Ilya S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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.
300 _aX, 158 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1561
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
856 4 0 _uhttps://doi.org/10.1007/BFb0073527
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9763
_d9763