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Complex stochastic processesan introduction to theory and application , Miller K.S. .pdf
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【成文时间】： 1974
【阅读语言】：英语
【页数】： 238
【作者】： Kenneth S. Miller
【文件格式】： pdf
【资料原名】：COMPLEX STOCHASTIC PROCESSES :An Introduction to Theory and Application
【摘要目录】：
COMPLEX STOCHASTIC PROCESSES
An Introduction to
Theory and Application
Kenneth S. Miller
Riverside Research Institute, New York, New York
Ў Ў
1974
Addison-Wesley Publishing Company, Inc.
Advanced Book Program
CONTENTS
PREFACE ix
I. CONVERGENCE OF RANDOM VARIABLES
0. Introduction 1
1. Sequences of Sets 2
2. Probability Space 6
3. Random Variables 10
4. Convergence with Probability One 14
5. Convergence in Probability 17
6. Convergence in Mean Square 19
7. Some Examples of Convergence 25
II. CONTINUITY OF RANDOM VARIABLES
0. Introduction 30
1. Stochastic Processes 31
2. Hermitian Matrices 32
3. Real Gaussian Distributions 35
4. Complex Gaussian Processes 38
5. The Spectral Distribution Function 42
6. Continuity of Sample Functions 48
7. Mean Square Continuity 55
8. Differentiability of Random Variables 58
9. Some Miscellaneous Results 67
III. THE COMPLEX DENSITY FUNCTION
0. Introduction 76
1. Complex Density Functions 77
2. Generating Functions 82
3. Distributions of Amplitudes and Phases 86
4. Some NnninU'itnil Moments and Moments of the Phases 92
IV. STOCHASTIC DIFFERENTIAL EQUATIONS
0. Introduction 101
1. Stochastic Integrals 102
2. Generalizations and Infinite Stochastic Integrals 109
3. Linear Differential Equations 120
4. Riemann-Stieltjes Integrals 125
5. Input-Output Covariances 131
6. Linear Difference Equations 134
7. Autoregressive Processes 136
V. ESTIMATION OF SIGNALS IN ADDITIVE NOISE
0. Introduction 139
1. An Elementary Example 139
2. Some Preliminary Results 141
3. The Estimation Problem 145
4. The Stochastic Model 146
5. Estimation of Random Signals 150
6. Estimation of Deterministic Signals 154
VI. SPECTRAL MOMENT ESTIMATION
0. Introduction 159
1. Spectral and Covariance Approaches 160
2. The Addition of Noise 166
3. Noncoherent Statistics 169
4. Statistics of the Spectral Moment Estimators 172
5. Mathematical Justification 179
VII. HYPOTHESIS TESTING
0. Introduction 187
1. The Likelihood Ratio Statistic 188
2. The Definite Case 192
3. The Indefinite Case 197
4. The Semidefinite Case 200
5. Some Additional Comments 203
VIII. COMPLEX LINEAR LEAST SQUARES
0. Introduction 208
1. The Basic Idea 209
2. Differentiation with Respect to a Matrix 210
3. The Normal Equation 212
4. The Gauss-Markov Theorem 213
5. Equivalence of Least Squares and Markov Estimates 216
6. Efficiency of the Least Squares Estimate 219
7. Maximum Likelihood Estimators 221
8. Regression Curves 226
REFERENCES 231
INDEX 235
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