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Najim K., Ikonen E., Daoud A.-K. — Stochastic processes. Estimation, optimization and analysis
Najim K., Ikonen E., Daoud A.-K. — Stochastic processes. Estimation, optimization and analysis

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Название: Stochastic processes. Estimation, optimization and analysis

Авторы: Najim K., Ikonen E., Daoud A.-K.

Аннотация:

For engineers dealing with stochastic processes and for students of automatic control and mechanical and electrical engineering, Najim (INP, Toulouse, France) Enso Ikonen (U. of Oulu, Finland) and Ait-Kadi Daoud (mechanical engineering, U. of Laval, Quebec) consider in turn stochastic processes, estimation, optimization, and the analysis of recursive stochastic algorithms to explain how to approach a variety of problems in applied probability and statistics. They emphasize the design of techniq ...


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 332

Добавлена в каталог: 13.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      321
Accuracy      178 253 255
Action probability distribution      174
Actions      174
Arrival counting process      64
atom      3
Backpropagation      144
Bayes      141 199
Bernoulli distribution      94 108
Beveridge — Nelson      18
Bias      138
Bienayme      24 154
Big-o      87
Binomial distribution      94 99 225 319
Blackwell Theorem      67
Boltzmann      212 213
Borel — Cantelli lemma      241 275 320
Borel, $\sigma$-algebra      13
Borel, function      14
Bush — Mosteller      179 181 185 278 279
Cauchy      42
Cauchy, distribution      105
Cauchy, sequence      82
Central limit theorem      101
Chapman — Kolmogorov equation      60
Characteristic function      35
chebyshev      133
Chernoff      201
Chi-squared distribution      154
Closed subset      53
Coefficient of correlation      23 31
Conditional mathematical expectation      27 28
Conditional probability      28
Confidence probability      196 199 201 203 204 207
Confidence probability, approximation      200
Conformity      153 155 156
Constraints      171 231
Convergence      231 254 261 288
Convergence rate      285 288 295 298
Convergence, almost surely      43 290 298
Convergence, in distribution      41 296
Convergence, in law      41
Convergence, in mean squares      43 240 293
Convergence, in probability      41 240
Convergence, in quadratic mean      43
Convergence, martingales      80
Convergence, with probability      1 43
Convex      34 76 87
Convolution      5 64 66 126
Covariance      22
Damping factor      171
De Morgan      2
Degrees of freedom      154 155
Differential equation      121
Discretization      178
Doob      75
Duflo      227
EA      214 (see “Evolutionary algorithms”)
Edgeworth      133
Eigenvalues      56 58
Eigenvectors      56 58
em      138 (see “Expectation Maximization”)
Encoding      215
Environment, binary      174
Environment, continuous      174
Environment, normalized response      182
Environment, P-model      174 179 203
Environment, response      174
Environment, S-model      174 179 189 203 225 254 263 270
Equality, almost surely      32
Equivalence relation      51
Ergodicity      18
Erlang distribution      111 117 148 153
Estimator, linear      30
Estimator, optimal      71
Event      3 12 28
Event, elementary      3 12
Evolutionary algorithms      214
Expectation      24
Expectation maximization      138 146
Expectation, conditional      27
Expectation, estimation      101
Exponential distribution      66 96 106 113
Exponential weighing      180
Fisher      154
Forgetting factor      264
Fourier transform      35
Fundamental matrix      53
GA      211 (see “Genetic algorithms”)
Galerkin      134
Gamma distribution      110 116 117
Gaussian      136 139
Gaussian, distribution      99 100 121 139 146 207
Gaussian, mixture      139
Generating function      36
Genetic algorithms      211 214 215
Geometric distribution      108
Gradient      289 301
Gradient, estimation      171
Greenwood and Nikulin      156
Grey coding      215
Hazard function      62 107 112
Helmert      154
hermite      133 134
Hybrid scheme      202 203 207 211
Hypergeometric distribution      95 319
I.o.      86
Identification      38
Inaction      176 179
Independence      39
Indicator function      10 28 243
Inequality, Bennett      236 237 319
Inequality, Boole      4
Inequality, Bunyakovsky — Schwartz      243
Inequality, Cauchy — Bounyakovsky      317
Inequality, Cauchy — Schwartz      254
Inequality, Chebyshev      240 241 243 304 318
Inequality, Cramer — Rao      138 305
Inequality, Edmundson — Madansky      34 244
Inequality, Hajek — Renyi      251 319
Inequality, Holder      315 317
Inequality, Jensen      76 244 278
Inequality, Kolmogorov      318
Inequality, Markov      318
Inequality, Minkovsky      316-317
Inequality, Schwartz      240 316
Inequality, submartingale      76
Inequality, triangle      155 315
Infinitely often      86
Infinum      84
Jointly stationary      17
Jordan decomposition      61
Kalman — Bucy      46
Kernel      134 139 140 148
Kernel, selection      140 148
Kiefer and Wolfowitz      168 229 232
Kolmogorov      6 148 156 250 324
Kolmogorov and Khinchin      248 250
kronecker      246 248 251
Kuhn — Tucker      172
kurtosis      117 140 147
Kushnerand Sanvicente      159
la      173 (see “Learning automata”)
Lagrange, function      159 171 228
Lagrange, multipliers      159 172 228
Laplace, distribution      104
Laplace, transform      35 66 115
Law of Large Numbers      18
Law of the iterated logarithm      325
Learning automata      173 189 254
Learning automata, team      270
Least squares method      22 137 154 231
Lebesgue      23 26—27
Lebesgue — Stieltjes (see “Lebesgue”)      27
legendre      133
Levenberg — Marquardt      145 149
Lifetime      64
Likelihood function      136 139
Likelihood function, log-likelihood      137
Likelihood function, negative log-likelihood      137 142 150
Limit of sequence      85
Lipschitz      178 253 290
Little-o      86
Lognormal distribution      102 127
Loss function      176 181 194 207
Lyapunov      226 270 280 281 291 297—299 323
Maintenance      188
Markov, aperiodic chain      55
Markov, chain      47 49 73 214
Markov, cyclic subclasses      57
Markov, diagram      50
Markov, ergodic chain      57
Markov, irreducible chain      53
Markov, periodic chain      54
Markov, probability transition matrix      48
Markov, property      17 47 51
Markov, return probability      54
Markov, stationary distribution      59
Markov, sub-chain      53
Markov, time      83
Markov, transition probability      48
Martingale      68 72
Martingale, difference sequence      83
Martingale, submartingale      69
Martingale, supermartingale      69
Maximum likelihood      136 139
McMurtry and Fu      180 224 255
Measurable      28
Memoryless      106 109
Metropolis      213
Mixing proportions      130
Mixture      135 148
Mixture density      130
Mixture, Gaussian      139
Model validation      153
Model-On-Demand      157
Moments      98 104 116 117 122 123 131 133
Moments, two random variables      22
Monte Carlo      141 214
Nadaraya      134
Nadaraya — Watson      134
Neural networks      143
Neural networks, one-hidden-layer sigmoid      144
Neveu      320
Newton binomial      94
Newton method      145 301
Nonstationary      17
Normal distribution      67 99 117 154 231 297 302 326
Normalization      181 197 198 202 203 273
Normalized excess      118
o      87
Observations      15
Optimal gain      301
Optimality      169
Ordinal optimization      200
Ordinary differential equation      232
Ordinary renewal process      67
Orthogonal      134
Orthogonal, sequence      37
Orthonormal      16 159
Parameter estimation      102
Partial sum      33 70
Parzen estimator      149
Passage probability      54
Pearson      123 154 155
Pearson distribution      154
Penalty      176 179 203
Penalty function      172
Penalty, function      184 228
Penalty, multipliers      184
Poisson, distribution      96 98 137 319
Poisson, process      17
Polyak and Juditsky      170
Population      214
Primitives      25
Probability density function      21
Probability density function, two random variables      22
probability distribution      20
Probability distribution, two random variables      22
Probability measure      13 174 204
Probability space      14
Projection      185 187 257 327
Pythagorean relation      82
Quantization      178
Random variable      14
Random variable, complex      127
Random variable, linear transformation      125
Random variable, measurable      15 27
Random variable, monotonic transformation      124
Random walk      15 18
Rayleigh distribution      109 113
Realization      15 16
Rectangular pulses      132
Regression      229
Regularized function      254 262
Regularizing factor      258
Reinforcement scheme      174
Reinforcement scheme, Bush — Mosteller      179
Reinforcement scheme, McMurtry — Fu      180 224 255
Reinforcement scheme, Shapiro — Narendra      179
Reinforcement scheme, Varashavskii — Vorontsova      225
Reliability      6 35 50 157 188
Reliability, function      62
Renewal, density      68
Renewal, equation      66
Renewal, function      65
Renewal, process      64 67
replacement      64 65 189 191
Representation      215 272
Reward      176 179 203
Riemann      25—27
Robbins and Monro      145 168 183 229 232 261
Robbins — Siegmund Theorem      228 249 253 275 280 284 292 323
Rosenblatt — Parzen      134 145
Ruppert — Polyak      302
Sa      211 (see “Simulated annealing”)
Sacks      296 325
Sample, mean      101
Sample, variance      101
SAT      168 (see “Stochastic approximation”)
Shapiro — Narendra      179 189 199 203 206
Sigma-algebra      12 13 27 174
Sigma-algebra, Borel      13
Sigma-algebra, increasing sequence      32
Sigmoid, function      144
Sigmoid, neural networks      143 144 149 202
Sigmoid, neural networks, gradients      144
simplex      182 185 257 327
Simulated annealing      211 212
skewness      117
SNN      143 (see “Sigmoid neural networks”)
Spectral decomposition      60
Stable distributions      37
State      46 50
State, absorbing      52 53
State, accessible      51
State, communicating      51 53
State, non-transient      53
State, null recurrent      54
State, positive recurrent      54
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