Process aleatoire
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Probability, Random Processes, and Ergodic Properties
Robert M. Gray Information Systems Laboratory Electrical Engineering Department Stanford University
Springer-Verlag New York
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c 1987 by Springer Verlag. Revised 2001 and 2006–2007 by Robert M. Gray.
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This book is affectionately dedicated to the memory of Elizabeth Dubois Jordan Gray 1906–1998 R. Adm. Augustine Heard Gray, U.S.N. 1888-1981 Sara Jean Dubois and William “Old Billy” Gray 1750-1825
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Contents
Contents Preface 1 Probability and Random Processes 1.1 Introduction . . . . . . . . . . . . . . . . . . 1.2 Probability Spaces and Random Variables . 1.3 Random Processes and Dynamical Systems 1.4 Distributions . . . . . . . . . . . . . . . . . 1.5 Extension . . . . . . . . . . . . . . . . . . . 1.6 Isomorphism . . . . . . . . . . . . . . . . . 2 Standard alphabets 2.1 Extension of Probability Measures . 2.2 Standard Spaces . . . . . . . . . . . 2.3 Some properties of standard spaces . 2.4 Simple standard spaces . . . . . . . . 2.5 Metric Spaces . . . . . . . . . . . . . 2.6 Extension in Standard Spaces . . . . 2.7 The Kolmogorov Extension Theorem 2.8 Extension Without a Basis . . . . . vii ix 1 1 1 6 8 13 19 21 21 22 26 29 31 36 37 38 45 45 48 54 61 61 61 64 67 77 80 87
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