Probability, Random Processes, and Ergodic Properties

1. Front Matter

   Pages i-xvi

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2. Probability and Random Processes

   • Robert M. Gray

   Pages 1-31

3. Standard Alphabets

   • Robert M. Gray

   Pages 32-65

4. Borel Spaces and Polish Alphabets

   • Robert M. Gray

   Pages 66-91

5. Averages

   • Robert M. Gray

   Pages 92-132

6. Conditional Probability and Expectation

   • Robert M. Gray

   Pages 133-172

7. Ergodic Properties

   • Robert M. Gray

   Pages 173-215

8. Ergodic Theorems

   • Robert M. Gray

   Pages 216-243

9. Process Metrics and the Ergodic Decomposition

   • Robert M. Gray

   Pages 244-283

10. Back Matter

    Pages 284-295

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This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature.

• average
• conditional probability
• probability
• time

• Department of Electrical Engineering, Stanford University, Stanford, USA

  Robert M. Gray

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