Studies In Probability And Ergodic Theory
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The Ergodic Theory Of Discrete Sample Paths
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Author : Paul C. Shields
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
The Ergodic Theory Of Discrete Sample Paths written by Paul C. Shields and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book is about finite-alphabet stationary processes, which are important in physics, engineering, and data compression. The focus is on the combinatorial properties of typical finite sample paths drawn from a stationary, ergodic process. A primary goal, only partially realized, is to develop a theory based directly on sample path arguments with minimal appeals to the probability formalism. A secondary goal is to give a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.
Dynamical Systems And Ergodic Theory
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Author : Mark Pollicott
language : en
Publisher:
Release Date : 2013-07-13
Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-13 with categories.
Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.
The Ergodic Theory Of Discrete Groups
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Author : Peter J. Nicholls
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-17
The Ergodic Theory Of Discrete Groups written by Peter J. Nicholls and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-17 with Mathematics categories.
The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.
Lectures On Ergodic Theory
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Author : Paul Richard Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1956
Lectures On Ergodic Theory written by Paul Richard Halmos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Mathematics categories.
This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.
Ergodic Theory
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Author : Karl E. Petersen
language : en
Publisher: Cambridge University Press
Release Date : 1989-11-23
Ergodic Theory written by Karl E. Petersen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-11-23 with Mathematics categories.
The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.
Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces
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Author : M. Bachir Bekka
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-11
Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces written by M. Bachir Bekka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-11 with Mathematics categories.
This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Mathematical Theory Of Entropy
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Author : Nathaniel F. G. Martin
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-02
Mathematical Theory Of Entropy written by Nathaniel F. G. Martin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Computers categories.
This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.
An Outline Of Ergodic Theory
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Author : Steven Kalikow
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-25
An Outline Of Ergodic Theory written by Steven Kalikow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-25 with Mathematics categories.
This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes, and various varieties of mixing. Original proofs of classic theorems - including the Shannon–McMillan–Breiman theorem, the Krieger finite generator theorem, and the Ornstein isomorphism theorem - are presented by degrees, together with helpful hints that encourage the reader to develop the proofs on their own. Hundreds of exercises and open problems are also included, making this an ideal text for graduate courses. Professionals needing a quick review, or seeking a different perspective on the subject, will also value this book.
Studies In Probability And Ergodic Theory
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Author : Gian-Carlo Rota
language : en
Publisher:
Release Date : 1978
Studies In Probability And Ergodic Theory written by Gian-Carlo Rota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Coupling methods for markov processes; On fluctuations of sums of random variables; Almost-sure invariance principle for branching brownian motion; On operator inequalities and projections; Boundary behavior of laplace-stieltjes transforms with applications to uniformly distributed sequences; Regularities of distribution; Strong liftings on topological measured spaces; Mixing transformations in an infinite measure space; On eventually weakly wandering sequences; Gap sequences and eventually weakly wandering sequences; The breakdown of automorphisms of compact topological groups; On the polynomial uniformity of translations on the n-torus; Generalized torus automorphisms are bernoullian; The isomorphism theorem for generalized Bernoulli Schemes; Measurabletransformations on homogeneous spaces; Ergodic transformations of lebesgue spaces.
Ergodic Behavior Of Markov Processes
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Author : Alexei Kulik
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-20
Ergodic Behavior Of Markov Processes written by Alexei Kulik and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Mathematics categories.
The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems