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Vanmarcke Erik — Random Fields : Analysis and Synthesis
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Íàçâàíèå: Random Fields : Analysis and SynthesisÀâòîð: Vanmarcke Erik Àííîòàöèÿ: Random variation over space and time is one of the few attributes that might safely be predicted as characterizing almost any given complex system. Random fields or "distributed disorder systems" confront astronomers, physicists, geologists, meteorologists, biologists, and other natural scientists. They appear in the artifacts developed by electrical, mechanical, civil, and other engineers. They even underlie the processes of social and economic change. The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient." Many new results and methods are included.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Âåðîÿòíîñòü /Ñòîõàñòè÷åñêèå ïðîöåññû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1983Êîëè÷åñòâî ñòðàíèö: 393Äîáàâëåíà â êàòàëîã: 15.06.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Adler, R. 150 170 Agriculture, applications in 2 266 Agterberg, F.P. 6 Aki, K. 6 Ambient sea noise 136 ARMA (autoregressive moving average) models 120 127—128 Atmospheric turbulence see "Turbulence" Autoregressive correlation models 120—128 178—179 186—187 193—194 274 303—305 see Axioan of probability 25 Bachelier, L. 4 68 Baggeroer, A.B. 136 Band-limited white noise 175—176 220 341 see Bandwidth measures see "Spectral bandwidth measures" Bartlett, M.S. 70 334 Batchelor, G.K. 7 84 195 Bath, M. 6 Bayes's theorem 27 29 30 52 Bayes's theorem, estimate of scale of fluctuation 327 346 Bayesian analysis 362 Belayev, Y.K. 170 316 Bendat, J.S. 7 Benjamin, J.R. 348 Beran, M.J. 7 Berg, J. 136 Berman, S.M. 164 Bernoulli random variables 63 67 Binary random fields 23 33—34 38 63—65 Binomial distribution 47 66—67 Biometrics, applications in 1 7 353 359—360 363 Blackman, R.B. 7 Bolotin, V.V. 7 Bolzmann's constant 72 73 359 Bounds on correlation function of isotropic fields 81 Bounds on moments of isotropic correlation functions 242 287—288 Bounds on spectral bandwidth measures 13 145—147 155 Bounds on spectral distribution function 140—141 Bracewell, R. 343 Brillinger, D.R. 7 Brockett, R. 5 Brownian motion 1 4 7 68 221 360 Brownian motion, Markov process and diffusion theory 69—73 Brownian motion, random walk 3 71—73 Brownian motion, scaling to render homogeneous 182 Bryson, A. 5 Business cycles, fluctuation of 358—359 Camp-Meidell inequality 141 Carrier function 150 Catastrophic failure 10 Caughey, T.K. 183 Central limit theorem 55—56 195 215 Chakravorty, M. 183 Chandiramani, K.L. 164 Chandrasekhar, S. 56 72 Chaos, spectral bandwidth measures of 17 219 Characteristic area 236 see Characteristic frequencies 139 Characteristic frequencies of local averages 211 Characteristic frequencies, examples 176—181 Characteristic functions 44—47 Characteristic functions, table 47 Chebyshev-type bounds on spectral distribution function 140—141 Chernov, L.A. 6 Chi-square distribution 47 Choot, G. 348 362 Churchman, C.W. 24 Circle noise 136 Circular symmetry see "Isotropy" Clarkson, B.L. 7 Cleary, M.P. 5 Clump size, mean 162 172 262 317 Clustering of level excursions and local maxima 161—163 172 262 317 319 Coefficient of correlation see "Covariance" Coefficient of variation 38 218 Coherence function 133 Communication engineering 4 7 Complex random process 88 100 108 151 Composite modeling 18 183 221—224 265 296 Composite modeling, parameter estimation 330—331 349 Conditional expectation in composite modeling 18 228 324 Conditional expectation in linear estimation 58—59 Conditional expectation, definitions 43—44 Conditional expectation, Gaussian 52—53 Conditional scale of fluctuation 247—250 291—295 248 Conditional scale of fluctuation, correlation function 250—251 296 Conditional scale of fluctuation, spectral density function 251—252 296 Conditional scale of fluctuation, variance function 247—250 291—295 Contour lines 165 170 Convolution, linear system response 106 Convolution, sums of two random variables 35 Cook, R.G. 164 Cornell, C.A. 348 Corner frequencies of frequency-dependent correlation measures 270—273 274 297—299 Corner frequencies of frequency-dependent variance function 278—279 Corotis, R.B. 183 Correlation function for white noise and purely random processes 63 64 Correlation function under local averaging 250 255—257 295 321 Correlation function, composite models 221 224—226 323 Correlation function, definition 10—11 41 79—84 Correlation function, estimation procedures 327 331—336 340 Correlation function, frequency-dependent 129—130 134—137 266 Correlation function, input-output for linear systems 105 109 Correlation function, lower bound, for isotropic fields 81 Correlation function, models from variance functions 181—186 Correlation function, moments 11—12 188 192—193 231 238 241—242 287 205—206 Correlation function, moving average and autoregressive (Markovian) 73 119—128 175 Correlation function, radial 81 103 242 274 287 299 see Correlation function, relationship to variance function 186 202 229 231 235 256 209 250 Correlation function, sensitivity to microscale variations 13—14 175 213 Correlation function, space-time 128—133 Correlation function, specific models 81—84 134—137 174—182 Correlation measures of composite models 222—224 265 323 Correlation measures of local averages 218 263 320 Correlation measures of sample spectral density function 341 347 Correlation measures of white noise 220—221 264 Correlation measures, existence conditions 237—239 240 287 Correlation measures, frequency-dependent 296—299 Correlation measures, notation 16 17 Correlation measures, three-dimensional 209—290 Correlation measures, two-dimensional 16 236 see Cospectrum 133 Covariance function see "Correlation function" Covariance matrix of a random vector 49—53 Covariance of local averages 201—202 231—232 253—256 290 205—209 Covariance of local averages and local deviations 227 223—224 Covariance of local spatial averages frequency dependent 280—282 Covariance of partial derivatives 149 167 169 Covariance, definition 39 Cramer, H. 12 136 151 164 166 170 Crandall, S.H. 7 65 164 Cross-covariance function 41 79—84 Cross-covariance function, matrix for vector field 84 Cross-spectral density function 11 89 101 Cross-spectral density function for input-output 109 348 Cross-spectral density function of spatial averages 279—283 Cross-spectral density function, space-time 129—133 34 Crossings see "Level excursion statistics" Cumulant functions 45—47 Cumulative distribution function, definition 27 Cumulative distribution function, spectral 87 96—97 103 Dam safety assessment 7—10 348 362 Damping coefficient 124 Data acquisition networks 19 282 347 350 351 353 361 362—363 Davenport, A.G. 163 Davenport, W.B. 7 De Haan, L. 36 Decay rate see "Reliability function" Decomposition of a random field 19 221—225 265 322—324 Decomposition of a random field through local averages 226—229 323—324 327—328 Degree of disorder, measures of 12 Degree of disorder, second law 17 see derivatives 110—114 see "Mean Desoer, C. 5 Differentiability see "Mean square differentiability" Diffusion 4—5 71—72 151 170 359—360 see Direction-dependent, correlation structure 82—83 239 245 Direction-dependent, local average processes 258—260 291—292 209 Direction-dependent, partial derivatives 148—149 168—169 259 309—312 Direction-dependent, random variation 239 245 Direction-dependent, scale of fluctuation 240 243 244 291—295 Direction-dependent, spatial random variation 130—131 Direction-dependent, spectra 11 95—96 239 244 Direction-dependent, threshold-crossing statistics 166—170 313—315 Direction-dependent, variance function 239 291 Direction-dependent, wave propagation 134—135 Directional see "Direction-dependent" Distances, probability density function 54 55 Distributed disordered systems 1—2 17 353 Distributed disordered systems, feedback and control 3 9—10 362—363 Distributed disordered systems, stochastic finite element analysis 17 253 340—347 Ditlevsen, O. 164 Downcrossing see "Level excursion statistics" Drake, A.W. 70 Duration of level excursion see "Level excursion statistics" Dwight, H.B. 48 122 Dyer, I. 82 Dynamic friction coefficient see "Brownian motion" Earthquake engineering 8 10 183 363 Econometrics, applications in 1 7 68 353—354 363 Einstein, A. 4 68—69 72 Ellipsoidal autoregressive models 123 244 Ellipsoidal correlation function 81—82 126—127 243 Ellipsoidal random fields 11 Ellipsoidal spectral density function 99 244 Envelope of local averages 213 261—262 314—315 316—317 see Envelope, basic statistics 150—155 Envelope, Cramer — Leadbetter 12 151 Envelope, excursion region, mean size of 167—169 217 261 314 Envelope, level crossing statistics and local maxima 160—162 171—172 217 262 316—317 Ergodicity in mean 118 195 Ergodicity in scale of fluctuation 346 Ergodicity, strict of modern fields 30 Estimation see "Optimal linear estimation" "Parameter Estimator for invariant 332 340 Estimator for scale of fluctuation 332 336 337 340 Estimator, variability 333—335 338—339 346 see Events 25 Events, simple events 26 Evolutionary spectra 183 Ewing, J.A. 83 Excursions, dimensions of excursion region 165—169 216—217 260—261 313—315 Excursions, mean rate for high threshold levels 170—172 215—216 261—262 315—317 Excursions, tendency for clustering 161—163 172—174 217 262 317 Expectation of random variables 37—44 Exponential law, correlation function 186 193—194 273 303 330 Exponential law, duration of stay below threshold 164 Exponential law, frequency-dependent correlation function 136 274 Exponential law, probability density function 47 Exponential law, relationship to Poisson process 74 see Exponential law, spectral density function 180—181 244 Exponential law, squared exponential correlation function 187 241 Extrapolation see "Optimal linear estimation" Extremes see "Maximum values" "Local "Reliability Feedback and control of distributed disorder systems 3 9—10 19 362—363 Feller, W. 4 70 75 159n Filtered Poisson process 77 Filtering see "Optimal linear estimation" Finite elements see "Stochastic finite element analysis" First passage distribution, multidimensional equivalent see "Reliability function" First passage distribution, one-dimensional 163—165 Fishman, G.S. 7 Fluid dynamics 6 7 see Fokker — Planck equation 4 72 see "Markov Fourier transform, characteristic function and probability density function 44—45 Fourier transform, cross-spectrum and cross-correlation function 89 101 Fourier transform, input-output relations for linear systems 106 Fourier transform, Parseval's theorem 343 Fourier transform, space-time correlation structure 131—132 266 Fourier transform, spectral density function and correlation function see also "Wiener — Khinchine relations" Fractional noise (1/f noise) 18 225 Fractional noise (1/f noise), spectral parameters 177 Frequency-dependent, spatial correlation function 129—130 266 296 Frequency-dependent, spatial correlation measures 296—300 Frequency-dependent, spatial cross-spectral density function 279—282 Frequency-dependent, spatial scale of fluctuation 267—273 273—275 Frequency-dependent, spatial variance function 276—380 300—303 Frequency-dependent, wave number spectrum 131—133 267 269 296 Galb, A. 7 124 Gamma distribution 26 47 74—75 Gaussian in Brownian motion 4 195 Gaussian, approximation for cumulative distribution function 49 Gaussian, central limit theorem 55—56 195 354 Gaussian, envelope statistics 151—155 Gaussian, fundamental limiting process 15 354 361 Gaussian, maxima and threshold-crossing statistics 155—162 169 173 Gaussian, model correlation function 187 242 Gaussian, moments of probability density function 48 51—52 Gaussian, probability density function, properties of 47 48—56 Gaussian, table of standard cumulative distribution function 50 Geol, N.S. 7 Geology, applications in 1 82 327 Geometric law, correlation function 121 230 Geometric law, probability mass function 67 Geometric mean of variances of directional derivatives 168—169 171 313 Geotechnology, applications in 8 10 327 348 362 Gnedenko, V.V. 36 Granger, C.W. 7 Grigori, M. 362 Gron, B. 136 Gumbel, E.J. 36 63 Hachich, W. 348 362 Hammond, J.K. 183 Hasofer, A.M. 170 Heal condition 70 see "Diffusion" Heisenberg's principle of uncertainty 8 Hilbert transform 151 Ho, Y. 5 Homogeneity of correlation structure 79 Homogeneity of random fields 10 31 Homogeneity, relationship to quadrant symmetry 80 Homogeneity, transforming nonhomogeneous fields 182—183 Hurst, H.E. 206 Hydrology 8 82 206 353 Impulse or point processes 4 Impulse or point processes, relation to local averages 219 Impulse or point processes, scale of fluctuation of 221 233 see Impulse or point processes, spectral representation of 91—92 Independence of events 26 Independence of increments in a counting process 65—68 Independence of purely random fields 62—65 Independence of random variables 29 45—46 Independence of sinusoidal components in spectral analysis 84 92 99 Independence, relation to correlation coefficient 51 Independent increments 65—68 Input-output relations, invariance in 217 262 319 Input-output relations, second-order for linear systems 105—110 Input-output relations, stochastic finite element analysis 253—255 348 Interpolation 56—57 see Invariant see also "Uncertainty density" Invariant in parameter estimation 328 Invariant in transport processes 360 Invariant, estimation from actual records 332—342 340 345—346 Invariant, first law of disorder 17 218 Invariant, frequency domain interpretation 344 Invariant, impulse process 92 220—221 223—224 233 Invariant, interpretation 15 218 221 Invariant, linear systems, input-output 217—218 262—264 319—320 Invariant, relation to diffusion coefficient 71—73 221 Invariant, relation to white noise 64 68—69 220—221 Ising model 5 Isotropic autoregressive correlation models 122—123 244
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