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Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness

  • Book
  • © 2001

Overview

Editors:
  1. Hubert Hennion

    1. I.R.M.A.R., University of Rennes 1, Rennes, France

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  2. Loïc Hervé

    1. I.R.M.A.R., University of Rennes 1, Rennes, France

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1766)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-V
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  2. General Facts About The Method Purpose Of The Paper

    Pages 1-5

  3. The Central Limit Theorems For Markov Chains Theorems A, B, C

    Pages 6-13

  4. Quasi-Compact Operators of Diagonal Type And Their Perturbations

    Pages 14-22

  5. First Properties of Fourier Kernels Application

    Pages 23-30

  6. Peripheral Eigenvalues of Fourier Kernels

    Pages 31-37

  7. Proofs Of Theorems A, B, C

    Pages 38-42

  8. Renewal Theorem For Markov Chains Theorem D

    Pages 43-48

  9. Large Deviations For Markov Chains Theorem E

    Pages 49-59

  10. Ergodic Properties For Markov Chains

    Pages 60-62

  11. Markov Chains Associated With Lipschitz Kernels Examples

    Pages 63-80

  12. Stochastic Properties Of Dynamical Systems Theorems A*, B*, C*, D*, E*

    Pages 81-88

  13. Expanding Maps

    Pages 89-98

  14. Proofs Of Some Statements In Probability Theory

    Pages 99-103

  15. Functional Analysis Results On Quasi-Compactness

    Pages 104-113

  16. Generalization To The Non-Ergodic Case

    • Loïc Herve
    Pages 115-140

  17. Back Matter

    Pages 141-145
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Keywords

About this book

The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.

Editors and Affiliations

  • I.R.M.A.R., University of Rennes 1, Rennes, France

    Hubert Hennion, Loïc Hervé

Bibliographic Information

  • Book Title: Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness

  • Editors: Hubert Hennion, Loïc Hervé

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b87874

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Softcover ISBN: 978-3-540-42415-4Published: 01 August 2001

  • eBook ISBN: 978-3-540-44623-1Published: 01 July 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 152

  • Topics: Probability Theory and Stochastic Processes, Analysis, Ordinary Differential Equations

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