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Rosenblatt M. — Random processes
Rosenblatt M. — Random processes



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Название: Random processes

Автор: Rosenblatt M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 217

Добавлена в каталог: 25.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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