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| Авторизация |
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| Поиск по указателям |
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| Miller K.S. — Complex stochastic processes |
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| Предметный указатель |
Additive set function 6
Almost certain convergence 14
Almost sure convergence 14
Approximating sum 102
Autoregressive process 134
Best linear unbiased estimate 214
Bhattacharyya coefficient 80
Bochner’s theorem 42
Borel field 6
Borel — Cantelli lemma 10
Casorati 134
Cauchy criterion 21
Cauchy criterion in distribution 18 72 109
Cauchy, criterion 21
Cauchy, distribution 88
Characteristic function 12 38 82 83
Chi-square distribution 224
Complex, density function 77
Complex, Gaussian density function 78
Complex, linear least squares (see Least squares)
Complex, random variable 14
Complex, signal 140
Complex, stochastic process 31
Continuity in mean square 55
Continuity of sample functions 48 55
Continuity with probability one 48
Contracting sequence 3
Convergence in mean square 19
Convergence in measure 17
Convergence in P-measure 17
Convergence in probability 17
Convergence in quadratic mean 19
Convergence of stochastic sequences 14 17 19
Convergence of stochastic series 23
Convergence with probability one 14
Convergence, almost everywhere 14
Convergence, Cauchy criterion 21
Correlation function 44
Covariance, function 31 69
Covariance, input-output 125
Covariance, matrix 35
Cramer — Rao lower bound 141
Critical region 188
Density function 13
Density function, complex Gaussian 78
Detection probability 188
Difference equation (see Linear difference equation)
Differentiability in mean square 62
Differentiability of sample functions 59
Differentiability with probability one 59
Differential equation (see Linear differential equation)
Differentiation with respect to a matrix 211
Distributed, identically 40
Distribution of amplitudes 87 89 92
Distribution of phases 88 89
Distribution, Cauchy 88
Distribution, convergence in 18 72 109
Distribution, function 10
Distribution, Gaussian 36 78
Distribution, joint 13
Distribution, normal 36 78
Distribution, Rayleigh 87
Distribution, spectral 44 136
Efficient statistic 141 153
Elliptic integral 97
Equivalent, random variables 14
Equivalent, stochastic processes 31
Ergodic property 119
Estimation of deterministic signals 154
Estimation of random signals 150
Estimation of spectral density 161
Estimation of spectral moments 159
Expanding sequence 3
Expectation 11
False alarm probability 188
Fisher information matrix 145
Frequency function 13
Function, characteristic 12 38 82 83
Function, complex Gaussian 78
Function, correlation 44
Function, covariance 31 69
Function, density 13
Function, distribution 10 13
Function, frequency 13
Function, generating 82
Function, left continuous 11
Function, likelihood 140 145 189 190
Function, mean 31
Function, measurable 10
Function, measure 6
Function, moment generating 37 84 85
Function, monotone 10
Function, nonnegative definite 12 31
Function, positive definite 31
Function, probability density 13
Function, regression 214 226
Function, right continuous 11
Function, sample 48
Function, set 6
Function, spectral distribution 44
Function, system 132 137
Gauss — Markov theorem 216
Gaussian distribution 36
Gaussian distribution, multivariate 36 78
Gaussian process, complex 38
Gaussian process, real 38
Generalized variance 229
Generating function 82
Green’s function 120 134
Grettenberg’s theorem 41
Hermitian matrix 32
Hermitian matrix, conjugate 32
Hermitian matrix, nonnegative definite 33
Hermitian matrix, positive definite 33
Hermitian matrix, skew 33
Hilbert space 20
Hypothesis testing 188
Identically distributed 40
Impulsive response 132 137
indefinite 197
Index set 31
Indicial polynomial 125 136
Inequality, Kantorovich 220
Inequality, Markov 118
Inequality, Schwarz 21
Inequality, triangle 21
Inequality, Tschebyscheff 16
Input-output covariance 125
Integral, mean square 103
Integral, Riemann — Stieltjes 11 125
Integral, sample function 103
Integral, Stochastic 103
Integral, stochastic, generalized 111
Integral, stochastic, infinite 114
Jacobi polynomial 86
Jacobi — Anger formula 94
Jacobi’s theorem 82
Kantorovich’s inequality 220
Karhunen — Loeve expansion 113
Lagrange multiplier 214
Laguerre polynomial 85
Least squares, dependent variables 212
Least squares, efficiency 219
Least squares, equivalence of estimates 217
Least squares, estimate 212
Least squares, Gauss — Markov theorem 216
Least squares, independent variables 212
Least squares, Markov estimate 215
Least squares, normal equation 213
Least squares, regression function 214 226
| Least squares, residual 214
Likelihood, equation 140
Likelihood, function 140 145 189 190
Likelihood, ratio statistic 191
Limit in the mean 20
Limit, inferior 2
Limit, superior 2
Linear difference equation 134
Linear difference equation, Casorati 134
Linear difference equation, Green’s function 134
Linear difference equation, impulsive response 137
Linear difference equation, indicial polynomial 136 137
Linear difference equation, stochastic 134
Linear difference equation, system function 137
Linear differential equation 120
Linear differential equation, Green’s function 120
Linear differential equation, impulsive response 132
Linear differential equation, indicial polynomial 125 132
Linear differential equation, stochastic 122
Linear differential equation, system function 132
Linear differential equation, Wronskian 121
Linear index set 31
Loeve criterion 21
Markov estimate 215
Markov inequality 118
Mathematical expectation 11
Matrix, covariance 35
Matrix, differentiability with respect to 211
Matrix, Fisher information 145
Matrix, hermitian 32
Matrix, indefinite 197
Matrix, negative definite 193
Matrix, negative semidefinite 200
Matrix, nonnegative definite 33 200
Matrix, nonpositive definite 200
Matrix, nonsingular 32
Matrix, positive definite 33
Matrix, positive semidefinite 200
Matrix, semidefinite 200
Matrix, skew-symmclric 2
Matrix, symmetric 32 34
Matrix, unitary 33
Maximum likelihood estimator 140 222
Mean, frequency 153
Mean, function 31
Mean, square continuity 55
Mean, square differentiability 62
Mean, square integral 103
Mean, square regression plane 227
Mean, vector 35
Measurable function 10
Measure function 6
Mercer’s theorem 112
Missed signal probability 188
Moment generating function 37 84 85
Moments of phases 94
Moments, nonintegral 92
Moments, spectral 153 159
Neumann addition formula 92
Neumann factor 92
Neyman — Pearson lemma 189
Nonintegral moments 92
Nonnegative definite 12 31 33 200
Nonpositive definite 200
Norm 102
Normal distribution 36
Normal distribution, multivariate 36 78
Normal equation 212 213
One-sided Green’s function 120 134
Parameter set 31
Parseval’s theorem 180
Partitfon 102
Positive definite 31 33
Power of the test 188
Power spectrum 44
Price’s theorem 81
Probability density function 13
Probability measure 6
Probability space 6
Process, stochastic (see Stochastic process)
Pulse-pair 188
Quadratic form 33
Quadratic form, nonnegative definite 33
Quadratic form, positive definite 33
Random process (see Stochastic process)
Random variable 10
Random variable, complex 14
Random variable, continuity 48
Random variable, differentiability 58
Random variable, equivalent 14
Rayleigh distribution 87
Regression, coefficients 226
Regression, curves 226
Regression, function 214 226
Regression, plane 227
Residual 214
Riemann — Stieltjes integral 11 125
Sample function 48
Sample function, continuity 48
Sample function, differentiability 59
Sample function, integral 103
Schwarz inequality 21
Semidefinite 200
Sequences of random variables 14
Sequences of random variables, Cauchy criterion 21
Sequences of random variables, Loeve criterion 21
Sequences of sets 2
Sequences of sets, contracting 3
Sequences of sets, expanding 3
Sequences of sets, limit 4
Sequences of sets, limit inferior 2
Sequences of sets, limit superior 2
Set, class 2
Set, empty 2
Set, function 6
Set, index 31
Set, sequence 2
Sigma-algebra 6
Simple hypothesis 188
Skew — Hermitian matrix 33
Space, abstract 6
Space, probability 6
Spectral density 44
Spectral distribution function 44 136
Spectral moment estimation, addition of noise 167
Spectral moment estimation, coherent 161 169
Spectral moment estimation, covariance approach 164
Spectral moment estimation, mathematical justification 179
Spectral moment estimation, noncoherent 169
Spectral moment estimation, spectral approach 164
Spectral moment estimation, statistics 174
Spectral moments 153 159
SPREAD 153
Stationary in the strict sense 32
Stationary in the wide sense 32
Stationary stochastic process 32
Stationary to the second order 32
Statistic, efficient 141 153
Statistic, spectral moment 174
Statistic, sufficient 141 223
Stochastic, autoregressive 134
Stochastic, complex 31
Stochastic, convergence 17
Stochastic, difference equation 134
Stochastic, differential equation 122
Stochastic, examples 25
Stochastic, Gaussian 38
Stochastic, generalized 111
Stochastic, infinite 114
Stochastic, integral 103
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