rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Limit theorems for unions of random closed sets
  name:
    name part: Molchanov, Ilya S.
    name part: 1962-
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1993
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (x, 157 pages) : illustrations.
  abstract: The 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.
  table of contents: 1. Distributions of random closed sets -- 2. Survey on stability of random sets and limit theorems for Minkowski addition -- 3. Infinite divisibility and stability of random sets with respect to unions -- 4. Limit theorems for normalized unions of random closed sets -- 5. Almost sure convergence of unions of random closed sets -- 6. Multivalued regularly varying functions and their application to limit theorems for unions of random sets -- 7. Probability metrics in the space of random sets distributions -- 8. Applications of limit theorems.
  note: Ilya S. Molchanov.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages [147]-152) and indexes.
  subject:
    topic: Geometric probabilities
  subject:
    topic: Limit theorems (Probability theory)
  subject:
    topic: Set theory
  subject:
    topic: Probabilités géométriques
  subject:
    topic: Théorèmes limites (Théorie des probabilités)
  subject:
    topic: Ensembles, Théorie des
  subject:
    topic: Geometric probabilities
  subject:
    topic: Limit theorems (Probability theory)
  subject:
    topic: Set theory
  subject:
    topic: Stochastische processen
  classification: QA3 .L28 no. 1561
  classification: QA273.5
  classification: 510 s 519.2
  classification: 31.00
  classification: 31.70
  related item:
    title info:
      title: Limit theorems for unions of random closed sets
    name:
      name part: Molchanov, Ilya S., 1962-
    origin info:
      publisher: Berlin ; New York : Springer-Verlag, ©1993
    identifier: (DLC) 93023595
    identifier: (OCoLC)28964291
  related item:
    title info:
      title: Lecture notes in mathematics (Springer-Verlag) ; 1561
  identifier: 9783540481119 (electronic bk.)
  identifier: 3540481117 (electronic bk.)
  identifier: 9780387573939
  identifier: 0387573933
  identifier: 9783540573937
  identifier: 3540573933
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: SPLNM
    record creation date: 090118
    record change date: 20260422154504.9
    record identifier: in00003505544
    language of cataloging:
      language term: eng