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: Stochastic and Integral Geometry
  name:
    name part: Schneider, Rolf.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Weil, Wolfgang.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 694 p. online resource.
  abstract: Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting.
  table of contents: Foundations of Stochastic Geometry -- Prolog -- Random Closed Sets -- Point Processes -- Geometric Models -- Integral Geometry -- Averaging with Invariant Measures -- Extended Concepts of Integral Geometry -- Integral Geometric Transformations -- Selected Topics from Stochastic Geometry -- Some Geometric Probability Problems -- Mean Values for Random Sets -- Random Mosaics -- Non-stationary Models -- Facts from General Topology -- Invariant Measures -- Facts from Convex Geometry.
  note: by Rolf Schneider, Wolfgang Weil.
  subject:
    topic: Mathematics
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Convex and Discrete Geometry
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Probability and Its Applications
  identifier: 9783540788591
  identifier: http://dx.doi.org/10.1007/978-3-540-78859-1
  record info:
    record creation date: 100301
    record change date: 20151204172649.0
    record identifier: 978-3-540-78859-1