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| Авторизация |
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| Rosenblatt M. — Random processes |
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| Предметный указатель |
Absolute continuity 86ff.
Absorbing barrier 43
Aggregation problem 62 67
Aliasing 151
Approximation 21ff. 33 35 76 168
Autoregressive scheme 164
Backward equation 125ff. 138 140 144ff.
Band-pass filter 196ff.
Bernstein polynomial 21ff. 33
Bias 170
Binomial distribution 13ff. 18ff. 33ff.
Birth and death process 133ff.
Borel field (= sigma-field) 68
Borel function 70
Borel set 69
Borel — Cantelli lemma 202
Branching process 42
Brownian motion 94 122 137ff.
Cauchy distribution 96
Central limit theorem 22ff. 33ff. 85ff. 97 200
Chapman — Kolmogorov equation 38 60 121 130ff. 133
Characteristic function 80ff. 97
Chebyshev's inequality 20
Closed set of states 52
Cointossing 12ff.
Conditional, expectation 89
Conditional, probability 10 87ff. 90 112ff.
Convergence in mean square 75
Convergence in probability 75
Convergence, almost everywhere 75
Convex function 34
Convolution 20 39
Countable additivity 9 69
Covariance 82
Covariance, function 149
Density function 78 86
Derivative 86ff.
Die 9ff.
Difference equations 152 163
Diffusion, equation 25 141
Diffusion, process 133ff.
Distribution function 23ff. 76ff. 89 91 96ff.
Distribution function, marginal 79
Eigenfunction 186
Eigenvalue of a matrix 45ff. 57 64
Eigenvalue of an integral equation 186
Eigenvector 45 57
Entropy of a stationary process 115ff.
Entropy of an experiment 29ff. 64
Entropy, conditional 29
Ergodic process 104ff. 109ff. 116 118 185
Ergodic theorem 102 105ff. 119 159 181
Expectation 15ff. 78 80
Exponential distribution 96
Field 8 72ff. 77
Fokker — Planck equation 137
Forward equation 125ff. 137ff. 142ff.
Fourier representation 153
Fourier transform 86
Fourier — Stieltjes transform 80 98 150
Frequency response function 153
Gaussian (= normal) 201
Generating function 18 33 39 53ff.
Growth process 39
Harmonic analysis (= Fourier analysis) 149
Heat equation 25
Independence of events 11 182
Independence of random variables 13 16 37 79 81 96ff. 110 183
Inner product 189
Input-output problem 66
integral 70ff.
Integral, equation 186ff.
Integral, random 156
Integral, Riemann — Stieltjes 78
Integrodifferential equation 125
Invariant function 105 107
Invariant set 105 108
Jensen's inequality 34
Jump process 124ff. 141ff.
Large numbers, law of 20ff.
Lebesgue measure 74
Lebesgue sets 73
Levy, P., inversion formula 86
m-step dependent process 118
Markov chain 36ff. 102 111ff. 119 130ff. 183 201
Markov chain, function of 59ff.
Markov chain, irreducible 52
Markov chain, reversible 63
| Markov process 120ff.
Markov property 36ff. 64 66 121ff.
Matrix 36
Matrix with non-negative elements 44ff.
Matrix, covariance 82
Matrix, irreducible 46
Matrix, positive definite 82
Mean 15
Measurability 69ff. 74
Measure-preserving transformation 103
Metric transitivity 105ff. 109
Mixing 110ff. 118
Mixing, uniform 195
Moment (= expectation) 15ff.
Moment (= expectation), factorial 18
Monte Carlo 98
Norm 191
Normal process 94 123 138 169
Normal random variable 79
Normal, jointly normal random variables 82ff. 90 97
Null state 53
Operator 190
Orthogonal increments, process of 156
Orthogonalization 161 187
Parabolic differential equation 135
Periodic state 53
Periodogram 170
Persistent state 53 65
Poisson, compound Poisson distribution 65
Poisson, distribution 14ff. 18ff. 33ff. 38
Poisson, process 94ff. 100 122ff.
Population model 39
Positive definite, function 149
Positive definite, matrix 82
Positive definite, sequence 151
Prediction 97 160ff. 181
Probability, measure 72
Probability, space 13 35 69
Random, phases, model of 151
Random, process 37 91ff.
Random, variable 13 37 69
Random, walk 42ff. 54 65
Recurrence time 52
Recurrence time, mean 52ff.
Recurrent state 53 66
Reflecting barrier 65
Sample, functions 93
Sample, points 8ff. 36 68 92
Sample, space 10
Semigroup 148
Separability 94
Shift transformation 103
Shot noise 100
Sigma-field 9 68ff.
Sigma-field, completed 72
Sigma-field, product 74
Spectral, density 150
Spectral, distribution function 150
Spectral, estimate 169ff.
State space of a Markov chain 36
State space of a Markov process 120
Stationary, process 44 100ff. 183
Stationary, transition mechanism 37 122
Stationary, weakly stationary process 149ff.
Statistical mechanics 101 119
Stochastic process 91
Theorems, Bochner 81
Theorems, Caratheodory 73
Theorems, Fubini 74
Theorems, Kolmogorov 92
Theorems, Liouville 102
Theorems, MacMillan 114ff.
Theorems, Mercer 202
Theorems, Radon — Nikodym 86ff.
Theorems, Riesz — Fisher 76
Theorems, Weierstrass 21 33
Toeplitz form 181
Transient response function 152
Transient state 53
Transition, matrix 37
Transition, probability function 121
Uniform, distribution 78
Uniform, integrability 72
Vector, extremal 47
Vector, invariant prob- ability 44
Vector-valued process 96 179ff.
Wiener process 94
Zero-one law 149ff.
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