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

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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.
Electronic books.
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
Description
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.
Physical Description:1 online resource (144 pages).
Bibliography:Includes bibliographical references (pages 141-144) and index.
ISBN:9783540446231
3540446230
9783540424154
3540424156
ISSN:0075-8434
;