Table of Contents
The ergodic theory of discrete sample paths
Preface
Chapter I. Basic concepts.
§I.1. Stationary processes.
§I.2. The ergodic theory model.
§I.3. The ergodic theorem.
§I.4. Frequencies of finite blocks.
§I.5. The entropy theorem.
§I.6. Entropy as expected value.
§I.7. Interpretations of entropy.
§I.8. Stationary coding.
§I.9. Process topologies.
§I.10. Cutting and stacking.
Chapter II. Entropy-related properties.
§II.1. Entropy and coding.
§II.2. The Lempel-Ziv algorithm.
§II.3. Empirical entropy.
§II.4. Partitions of sample paths.
§II.5. Entropy and recurrence times.
Chapter III. Entropy for restricted classes.
§III.1. Rates of convergence.
§III.2. Entropy and joint distributions.
§III.3. The dbar-admissibility problem.
§III.4. Blowing-up properties.
§III.5. The waiting-time problem.
Chapter IV. B-processes.
§IV.1. Almost block-independence.
§IV.2. The finitely determined property.
§IV.3. Other B-process characterizations.
Bibliography
Index
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