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The Ergodic Theory of Discrete Sample Paths
 
Front Cover for The Ergodic Theory of Discrete Sample Paths
Available Formats:
Hardcover ISBN: 978-0-8218-0477-3
Product Code: GSM/13
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $42.40
Electronic ISBN: 978-1-4704-2071-0
Product Code: GSM/13.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
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Front Cover for The Ergodic Theory of Discrete Sample Paths
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  • Front Cover for The Ergodic Theory of Discrete Sample Paths
  • Back Cover for The Ergodic Theory of Discrete Sample Paths
The Ergodic Theory of Discrete Sample Paths
Available Formats:
Hardcover ISBN:  978-0-8218-0477-3
Product Code:  GSM/13
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $42.40
Electronic ISBN:  978-1-4704-2071-0
Product Code:  GSM/13.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50
MAA Member Price: $71.55
AMS Member Price: $63.60
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 131996; 249 pp
    MSC: Primary 28; 94; Secondary 60;



    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.

    Features:

    • Emphasis on recent combinatorial results about sample paths.
    • Careful treatment of many models found to be useful in engineering.
    • Applications of entropy ideas to coding, sample path structure, distribution estimation, recurrence times, waiting times, and prefix trees.
    • Simplification, adaptation, and updating to the process setting of Ornstein isomorphism theory.

    Readership

    Graduate students and faculty members in mathematics, engineering, statistics, and physics who are interested in measure theory and probability theory.

  • Table of Contents
     
     
    • Chapters
    • Chapter I. Basic concepts
    • Chapter II. Entropy-related properties
    • Chapter III. Entropy for restricted classes
    • Chapter IV. B-processes
  • Reviews
     
     
    • A very original book on a topic of current interest written by an experienced author.

      Zentralblatt MATH
    • This is a well-written book. Being an expert in the field, the author has chosen his own way of organization and presentation of the material. The result is a unique book with many interesting details for the expert and a text for the graduate student which is well thought out … covers important and useful aspects of probabilistic discrete-sample-paths theory.

      Mathematical Reviews
    • This is an interesting and well-written account of the ergodic theory of stationary processes from the viewpoint of entropy theory. This book is a beautiful and very readable treatment of an important part of ergodic theory. It is written by an expert in the field who has made very significant contributions and who has an excellent knowledge of the great relevance of the theory to other fields such as information theory … strongly recommend this book to anyone who is interested in ergodic theory, stochastic processes or information theory.

      Bulletin of the London Mathematical Society
  • Request Review Copy
  • Get Permissions
Volume: 131996; 249 pp
MSC: Primary 28; 94; Secondary 60;



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.

Features:

  • Emphasis on recent combinatorial results about sample paths.
  • Careful treatment of many models found to be useful in engineering.
  • Applications of entropy ideas to coding, sample path structure, distribution estimation, recurrence times, waiting times, and prefix trees.
  • Simplification, adaptation, and updating to the process setting of Ornstein isomorphism theory.

Readership

Graduate students and faculty members in mathematics, engineering, statistics, and physics who are interested in measure theory and probability theory.

  • Chapters
  • Chapter I. Basic concepts
  • Chapter II. Entropy-related properties
  • Chapter III. Entropy for restricted classes
  • Chapter IV. B-processes
  • A very original book on a topic of current interest written by an experienced author.

    Zentralblatt MATH
  • This is a well-written book. Being an expert in the field, the author has chosen his own way of organization and presentation of the material. The result is a unique book with many interesting details for the expert and a text for the graduate student which is well thought out … covers important and useful aspects of probabilistic discrete-sample-paths theory.

    Mathematical Reviews
  • This is an interesting and well-written account of the ergodic theory of stationary processes from the viewpoint of entropy theory. This book is a beautiful and very readable treatment of an important part of ergodic theory. It is written by an expert in the field who has made very significant contributions and who has an excellent knowledge of the great relevance of the theory to other fields such as information theory … strongly recommend this book to anyone who is interested in ergodic theory, stochastic processes or information theory.

    Bulletin of the London Mathematical Society
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