文档介绍：Probability,
Random Processes,
and Ergodic Properties
November 3, 2001
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Probability,
Random Processes,
and Ergodic Properties
Robert M. Gray
Information Systems Laboratory
Department of Electrical Engineering
Stanford University
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°c 1987 by Springer Verlag, 2001 revision by Robert M. Gray.
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This book is affectionately dedicated to
Elizabeth Dubois Jordan Gray
and to the memory of
R. Adm. Augustine Heard Gray, .
1888-1981
Sara Jean Dubois
and
William “Billy” Gray
1750-1825
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Preface
History and Goals
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, probability
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 inclined 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 discourage them from the second part. Hence I finally followed a 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 had merit as filling a unique, albeit small,
hole in the literature. Personal experience indicates that the intended audience rarely has the time to
take plete course in measure and probability