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

• Main Authors: Hennion, Hubert (Author, http://id.loc.gov/vocabulary/relators/aut), Herve, Loic (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1766
• Subjects: Probabilities.; Mathematical analysis.; Analysis (Mathematics).; Differential equations.; Probability Theory and Stochastic Processes.; Analysis.; Ordinary Differential Equations.

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 operat...

Table of 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.