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. … strongly recommend this book to anyone who is interested in ergodic theory, stochastic processes or information theory.

—Bulletin of the London Mathematical Society

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.

The book has many attractive features for both students and researchers. An emphasis is placed on recent combinatorial results for sample paths. There are careful treatments of many models that have been found to be useful in engineering. Shields covers applications of entropy ideas to coding, sample path structure, distribution estimation, recurrence times, waiting times, and prefix trees.

Readership

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