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- catalog abstract "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.".
- catalog contributor b12290077.
- catalog contributor b12290078.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description "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. Hervé).".
- catalog description "Includes bibliographical references (p. [141]-144) and indexes.".
- catalog description "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.".
- catalog extent "144 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540424156 (pbk. : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1766.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1766".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 519.2/33 21".
- catalog subject "Differentiable dynamical systems.".
- catalog subject "Differential Equations.".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Limit theorems (Probability theory)".
- catalog subject "Markov processes.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1766 QA274.7".
- catalog subject "Stochastic processes.".
- catalog tableOfContents "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. Hervé).".
- catalog title "Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness / Hubert Hennion, Loïc Hervé.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".