Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness / edited by Hubert Hennion, Loïc Hervé.

Format:

Book

Contributor:

Hennion, Hubert, 1944- editor.

Hervé, Loïc, 1963- editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1766.

Lecture Notes in Mathematics, 0075-8434 ; 1766

Language:

English

Subjects (All):

Distribution (Probability theory).

Global analysis (Mathematics).

Differential equations.

Probability Theory and Stochastic Processes.

Analysis.

Ordinary Differential Equations.

Local Subjects:

Probability Theory and Stochastic Processes.

Analysis.

Ordinary Differential Equations.

Physical Description:

1 online resource (VIII, 152 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2001.

System Details:

text file PDF

Summary:

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.

Contents:

General Facts About The Method Purpose Of The Paper

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

Quasi-Compact Operators of Diagonal Type And Their 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

Markov Chains Associated With Lipschitz Kernels Examples

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

Expanding Maps

Proofs Of Some Statements In Probability Theory

Functional Analysis Results On Quasi-Compactness

Generalization To The Non-Ergodic Case.

Other Format:

Printed edition:

ISBN:

9783540446231

Access Restriction:

Restricted for use by site license.