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Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness /

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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 tre...

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Bibliographic Details
Main Author: Hennion, Hubert, 1944-
Corporate Author: SpringerLink (Online service)
Other Authors: Hervé, Loïc, 1963-
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [2001]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1766.
Subjects:
Markov processes.
Limit theorems (Probability theory)
Differentiable dynamical systems.
Stochastic processes.
Electronic books.
Online Access:Connect to the full text of this electronic book
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).