Probability, Random Processes, and Ergodic Properties

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Springer-Verlag, 1988 - Mathematics - 295 pages
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This book is a self-contained treatment of the theory of probability, random processes. It is intended to lay solid theoretical foundations for advanced probability, that is, for measure and integration theory, and to develop in depth the long term time average behavior of measurements made on random processes with general output alphabets. Unlike virtually all texts on the topic, considerable space is devoted to processes that violate the usual assumptions of stationarity and ergodicity, yet which still possess the fundamental properties of convergence of long term averages to appropriate expectations. The theory of asymtotically mean stationary processes and the ergodic decomposition are both treated in depth for both one-sided and two-sided random processes. In addition, the book treats many of the fundamental results such as the Kolmogorov extension theorem and the ergodic decomposition theorem. Much of the material has not previously appeared in book form, and the treatment takes advantage of many recent generalizations and simplifications.

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Contents

PROBABILITY AND RANDOM PROCESSES
1
SPACES OF MEASURES
8
STANDARD ALPHABETS
32
Copyright

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About the author (1988)

Robert M. Gray received his PhD from the University of Southern California, and is Professor and Vice Chair of Electrical Engineering at Stanford University. He has written over 200 scientific papers in areas including information theory, applied probability, signal processing, speech and image processing and coding, ergodic thoery, and the theory of Toeplitz matrices. He is a Fellow of the IEEE and the Institute of Mathematical Statistics.

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