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

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

Saved in:

Bibliographic Details
Author / Creator:	Hennion, Hubert, 1944-
Imprint:	Berlin ; New York : Springer, ©2001.
Description:	1 online resource (144 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1766 Lecture notes in mathematics (Springer-Verlag) ; 1766.
Subject:	Markov processes. Limit theorems (Probability theory) Differentiable dynamical systems. Stochastic processes. Differentiable dynamical systems. Limit theorems (Probability theory) Markov processes. Stochastic processes.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11064939

Hidden Bibliographic Details
Other authors / contributors:	Hervé, Loïc, 1963-
ISBN:	9783540446231 3540446230 9783540424154 3540424156
Notes:	Includes bibliographical references (pages 141-144) and index. Print version record.
Summary:	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.
Other form:	Print version: Hennion, Hubert, 1944- Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness. Berlin ; New York : Springer, ©2001 3540424156

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).