LEADER 03785nam 2200601 450 001 996466376703316 005 20220908070557.0 010 $a3-540-48111-7 024 7 $a10.1007/BFb0073527 035 $a(CKB)1000000000437162 035 $a(SSID)ssj0000324435 035 $a(PQKBManifestationID)12098550 035 $a(PQKBTitleCode)TC0000324435 035 $a(PQKBWorkID)10314194 035 $a(PQKB)11233626 035 $a(DE-He213)978-3-540-48111-9 035 $a(MiAaPQ)EBC5592338 035 $a(Au-PeEL)EBL5592338 035 $a(OCoLC)1066184823 035 $a(MiAaPQ)EBC6842128 035 $a(Au-PeEL)EBL6842128 035 $a(PPN)155221159 035 $a(EXLCZ)991000000000437162 100 $a20220908d1993 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLimit theorems for unions of random closed sets /$fIlya S. Molchanov 205 $a1st ed. 1993. 210 1$aBerlin :$cSpringer-Verlag,$d[1993] 210 4$dİ1993 215 $a1 online resource (X, 158 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1561 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57393-3 327 $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. 330 $aThe book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1561. 606 $aGeometric probabilities 606 $aLimit theorems (Probability theory) 615 0$aGeometric probabilities. 615 0$aLimit theorems (Probability theory) 676 $a519.2 700 $aMolchanov$b Ilya S.$f1962-$01255119 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466376703316 996 $aLimit theorems for unions of random closed sets$92910205 997 $aUNISA