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Najim K., Ikonen E., Daoud A.-K. — Stochastic processes. Estimation, optimization and analysis
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Название: Stochastic processes. Estimation, optimization and analysisАвторы: 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: Рубрика: Технология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 332Добавлена в каталог: 13.10.2005Операции: Положить на полку |
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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, 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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