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 Markov chains and stochastic properties of dynamical systems by quasi-compactness
  name:
    name part: Hennion, Hubert
    name part: 1944-
    role:
      role term: creator
  name:
    name part: Hervé, Loïc
    name part: 1963-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 2001
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (144 pages)
  abstract: This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
  table of contents: General facts about the method, purpose of the paper -- The central limit theorems for Markov chains -- Quasi-compact operators of diagonal type and perturbations -- First properties of Fourier kernels, application -- Peripheral eigenvalues of Fourier kernels -- Proofs of theorems A, B, C -- Renewal theorem for Markov chains (theorem D) -- Large deviations for Markov chains (theorem E) -- Ergodic properties for Markov chains -- Stochastic properties of dynamical systems -- Expanding maps -- Proofs of some statements in probability theory -- Functional analysis results on quasi-compactness -- Generalization to the non-ergodic case (by L. Herv).
  target audience: specialized
  note: Hubert Hennion, Loïc Hervé.
  note: Electronic resource.
  note: Includes bibliographical references (pages [141]-144) and index.
  subject:
    topic: Markov processes
  subject:
    topic: Limit theorems (Probability theory)
  subject:
    topic: Differentiable dynamical systems
  subject:
    topic: Stochastic processes
  subject:
    topic: Differentiable dynamical systems
  subject:
    topic: Limit theorems (Probability theory)
  subject:
    topic: Markov processes
  subject:
    topic: Stochastic processes
  classification: QA3 .L28 no. 1766
  classification: 510 s 519.2/33
  related item:
    title info:
      title: Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
    name:
      name part: Hennion, Hubert, 1944-
    origin info:
      publisher: Berlin ; New York : Springer, ©2001
    identifier: (DLC) 2001044646
    identifier: (OCoLC)47805084
  related item:
    title info:
      title: Lecture notes in mathematics (Springer-Verlag) ; 1766
  identifier: 9783540446231 (electronic bk.)
  identifier: 3540446230 (electronic bk.)
  identifier: 9783540424154
  identifier: 3540424156
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: EYM
    record creation date: 020620
    record change date: 20260422230148.0
    record identifier: in00003514210
    language of cataloging:
      language term: eng