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Vanmarcke Erik Ч Random Fields : Analysis and Synthesis
Vanmarcke Erik Ч Random Fields : Analysis and Synthesis

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Ќазвание: Random Fields : Analysis and Synthesis

јвтор: Vanmarcke Erik

јннотаци€:

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.

After outlining the extent and characteristics of the random field approach, the book reviews the classical theory of multidimensional random processes and introduces basic probability concepts and methods in the random field context. It next gives a concise amount of the second-order analysis of homogeneous random fields, in both the space-time domain and the wave number-frequency domain. This is followed by a chapter on spectral moments and related measures of disorder and on level excursions and extremes of Gaussian and related random fields.

After developing a new framework of analysis based on local averages of one-, two-, and n-dimensional processes, the book concludes with a chapter discussing ramifications in the important areas of estimation, prediction, and control. The mathematical prerequisite has been held to basic college-level calculus.


язык: en

–убрика: ћатематика/¬еро€тность/—тохастические процессы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1983

 оличество страниц: 393

ƒобавлена в каталог: 15.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
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 127Ч128
Atmospheric turbulence      see "Turbulence"
Autoregressive correlation models      120Ч128 178Ч179 186Ч187 193Ч194 274 303Ч305 see
Axioan of probability      25
Bachelier, L.      4 68
Baggeroer, A.B.      136
Band-limited white noise      175Ч176 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 33Ч34 38 63Ч65
Binomial distribution      47 66Ч67
Biometrics, applications in      1 7 353 359Ч360 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 287Ч288
Bounds on spectral bandwidth measures      13 145Ч147 155
Bounds on spectral distribution function      140Ч141
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      69Ч73
Brownian motion, random walk      3 71Ч73
Brownian motion, scaling to render homogeneous      182
Bryson, A.      5
Business cycles, fluctuation of      358Ч359
Camp-Meidell inequality      141
Carrier function      150
Catastrophic failure      10
Caughey, T.K.      183
Central limit theorem      55Ч56 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      176Ч181
Characteristic functions      44Ч47
Characteristic functions, table      47
Chebyshev-type bounds on spectral distribution function      140Ч141
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      161Ч163 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 221Ч224 265 296
Composite modeling, parameter estimation      330Ч331 349
Conditional expectation in composite modeling      18 228 324
Conditional expectation in linear estimation      58Ч59
Conditional expectation, definitions      43Ч44
Conditional expectation, Gaussian      52Ч53
Conditional scale of fluctuation      247Ч250 291Ч295 248
Conditional scale of fluctuation, correlation function      250Ч251 296
Conditional scale of fluctuation, spectral density function      251Ч252 296
Conditional scale of fluctuation, variance function      247Ч250 291Ч295
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      270Ч273 274 297Ч299
Corner frequencies of frequency-dependent variance function      278Ч279
Corotis, R.B.      183
Correlation function for white noise and purely random processes      63 64
Correlation function under local averaging      250 255Ч257 295 321
Correlation function, composite models      221 224Ч226 323
Correlation function, definition      10Ч11 41 79Ч84
Correlation function, estimation procedures      327 331Ч336 340
Correlation function, frequency-dependent      129Ч130 134Ч137 266
Correlation function, input-output for linear systems      105 109
Correlation function, lower bound, for isotropic fields      81
Correlation function, models from variance functions      181Ч186
Correlation function, moments      11Ч12 188 192Ч193 231 238 241Ч242 287 205Ч206
Correlation function, moving average and autoregressive (Markovian)      73 119Ч128 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      13Ч14 175 213
Correlation function, space-time      128Ч133
Correlation function, specific models      81Ч84 134Ч137 174Ч182
Correlation measures of composite models      222Ч224 265 323
Correlation measures of local averages      218 263 320
Correlation measures of sample spectral density function      341 347
Correlation measures of white noise      220Ч221 264
Correlation measures, existence conditions      237Ч239 240 287
Correlation measures, frequency-dependent      296Ч299
Correlation measures, notation      16 17
Correlation measures, three-dimensional      209Ч290
Correlation measures, two-dimensional      16 236 see
Cospectrum      133
Covariance function      see "Correlation function"
Covariance matrix of a random vector      49Ч53
Covariance of local averages      201Ч202 231Ч232 253Ч256 290 205Ч209
Covariance of local averages and local deviations      227 223Ч224
Covariance of local spatial averages frequency dependent      280Ч282
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 79Ч84
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      279Ч283
Cross-spectral density function, space-time      129Ч133 34
Crossings      see "Level excursion statistics"
Cumulant functions      45Ч47
Cumulative distribution function, definition      27
Cumulative distribution function, spectral      87 96Ч97 103
Dam safety assessment      7Ч10 348 362
Damping coefficient      124
Data acquisition networks      19 282 347 350 351 353 361 362Ч363
Davenport, A.G.      163
Davenport, W.B.      7
De Haan, L.      36
Decay rate      see "Reliability function"
Decomposition of a random field      19 221Ч225 265 322Ч324
Decomposition of a random field through local averages      226Ч229 323Ч324 327Ч328
Degree of disorder, measures of      12
Degree of disorder, second law      17 see
derivatives      110Ч114 see "Mean
Desoer, C.      5
Differentiability      see "Mean square differentiability"
Diffusion      4Ч5 71Ч72 151 170 359Ч360 see
Direction-dependent, correlation structure      82Ч83 239 245
Direction-dependent, local average processes      258Ч260 291Ч292 209
Direction-dependent, partial derivatives      148Ч149 168Ч169 259 309Ч312
Direction-dependent, random variation      239 245
Direction-dependent, scale of fluctuation      240 243 244 291Ч295
Direction-dependent, spatial random variation      130Ч131
Direction-dependent, spectra      11 95Ч96 239 244
Direction-dependent, threshold-crossing statistics      166Ч170 313Ч315
Direction-dependent, variance function      239 291
Direction-dependent, wave propagation      134Ч135
Directional      see "Direction-dependent"
Distances, probability density function      54 55
Distributed disordered systems      1Ч2 17 353
Distributed disordered systems, feedback and control      3 9Ч10 362Ч363
Distributed disordered systems, stochastic finite element analysis      17 253 340Ч347
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 353Ч354 363
Einstein, A.      4 68Ч69 72
Ellipsoidal autoregressive models      123 244
Ellipsoidal correlation function      81Ч82 126Ч127 243
Ellipsoidal random fields      11
Ellipsoidal spectral density function      99 244
Envelope of local averages      213 261Ч262 314Ч315 316Ч317 see
Envelope, basic statistics      150Ч155
Envelope, Cramer Ч Leadbetter      12 151
Envelope, excursion region, mean size of      167Ч169 217 261 314
Envelope, level crossing statistics and local maxima      160Ч162 171Ч172 217 262 316Ч317
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      333Ч335 338Ч339 346 see
Events      25
Events, simple events      26
Evolutionary spectra      183
Ewing, J.A.      83
Excursions, dimensions of excursion region      165Ч169 216Ч217 260Ч261 313Ч315
Excursions, mean rate for high threshold levels      170Ч172 215Ч216 261Ч262 315Ч317
Excursions, tendency for clustering      161Ч163 172Ч174 217 262 317
Expectation of random variables      37Ч44
Exponential law, correlation function      186 193Ч194 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      180Ч181 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 9Ч10 19 362Ч363
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      163Ч165
Fishman, G.S.      7
Fluid dynamics      6 7 see
Fokker Ч Planck equation      4 72 see "Markov
Fourier transform, characteristic function and probability density function      44Ч45
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      131Ч132 266
Fourier transform, spectral density function and correlation function      see also "Wiener Ч Khinchine relations"
Fractional noise (1/f noise)      18 225
Fractional noise (1/f noise), spectral parameters      177
Frequency-dependent, spatial correlation function      129Ч130 266 296
Frequency-dependent, spatial correlation measures      296Ч300
Frequency-dependent, spatial cross-spectral density function      279Ч282
Frequency-dependent, spatial scale of fluctuation      267Ч273 273Ч275
Frequency-dependent, spatial variance function      276Ч380 300Ч303
Frequency-dependent, wave number spectrum      131Ч133 267 269 296
Galb, A.      7 124
Gamma distribution      26 47 74Ч75
Gaussian in Brownian motion      4 195
Gaussian, approximation for cumulative distribution function      49
Gaussian, central limit theorem      55Ч56 195 354
Gaussian, envelope statistics      151Ч155
Gaussian, fundamental limiting process      15 354 361
Gaussian, maxima and threshold-crossing statistics      155Ч162 169 173
Gaussian, model correlation function      187 242
Gaussian, moments of probability density function      48 51Ч52
Gaussian, probability density function, properties of      47 48Ч56
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      168Ч169 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      182Ч183
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      91Ч92
Independence of events      26
Independence of increments in a counting process      65Ч68
Independence of purely random fields      62Ч65
Independence of random variables      29 45Ч46
Independence of sinusoidal components in spectral analysis      84 92 99
Independence, relation to correlation coefficient      51
Independent increments      65Ч68
Input-output relations, invariance in      217 262 319
Input-output relations, second-order for linear systems      105Ч110
Input-output relations, stochastic finite element analysis      253Ч255 348
Interpolation      56Ч57 see
Invariant      see also "Uncertainty density"
Invariant in parameter estimation      328
Invariant in transport processes      360
Invariant, estimation from actual records      332Ч342 340 345Ч346
Invariant, first law of disorder      17 218
Invariant, frequency domain interpretation      344
Invariant, impulse process      92 220Ч221 223Ч224 233
Invariant, interpretation      15 218 221
Invariant, linear systems, input-output      217Ч218 262Ч264 319Ч320
Invariant, relation to diffusion coefficient      71Ч73 221
Invariant, relation to white noise      64 68Ч69 220Ч221
Ising model      5
Isotropic autoregressive correlation models      122Ч123 244
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