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Adomian G. — Stochastic Systems

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Название: Stochastic Systems

Автор: Adomian G.

Аннотация:

The mathematical method is easy to describe. One constructs a mathematical model of a system or part of a system. Then one uses mathematical methods to study the equations that result. Finally, one interprets the results with respect to the original system.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 331

Добавлена в каталог: 13.12.2009

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Предметный указатель

Abel’s constant      12
Abel’s formula      10 15 16
Abstract structure      298
Acceleration of convergence      188
Adjoint operators      20 22 23 92 102 120 154
Adomian solution      209
Analytic expansions      215
Analytic parametrization      215
Analytic solution      207 208
Approximate correlation      195
Approximate mean solution      194
Arbitrary deterministic nonlinear function      159
Autocorrelation function      161
Average operator      105
Averaged equation      105
Black Box      7
Borel field      60
boundary conditions      8 11 13
Brownian motion      58 64 98 307
Canonical expansion      245
Cartesian product      100
Causality      6
Central moment      67
Characteristic function      70 72
Chebyshev — Hermite expansion      286 294 301
Closure approximation      103 104 107 108 109 114 157
Comparison of solutions      206
Compartment models      315
Computational aspects      201
Consistency condition      61
Continuity      74
Continuity (integrability)      139
Convergence      73 112 131 159 164 187 189 221 302 311
Correlation      64 68 70 77 250
Correlation function      76 79
Correlation of order n      274
Covariance      68
Covariance function      69 213
Cubic case      165
Cumulative distribution function      59
Decomposition      121 135 226
Decomposition method      119 134 152 186 201 208 230 232 314
derivatives      74
Deterministic      2
Deterministic limit      225
Deterministic nonlinear equation      159 268
Deterministic operator      99
Deterministic system      97
Dirac delta      111
Dirac delta function      5 105
Dirac measure      106
dispersion      68
Dispersion of order      273
distribution      24 61 62 73
Distribution function      61
Dynamical system      1
Eigenvalue equation      76
Elementary random function      246
Ensemble      60
Ergodic hypothesis      66
Ergodic in correlation of order      280
Ergodic in mean square of order      280
Ergodic in the mean of order n      279
Ergodic process      65
Ergodic theorem      77 78
Ergodicity      77 78
Ergodicity of order h      273
Euclidean space      80
Events      59
Existence      230 303
Expansion coefficients      218
Expectation      66 72 113
Expectation of order h      273 293
Exponential nonlinearity      170 204
Field of events      59
Filter      7 79
First-order improvement      187 188 192
First-stage approximation      202
Fourier coefficients      77
Fourier series      4 75 221
Fourier transform      88 288
Fourth power case      165
Fourth-stage approximation      203
Fubini’s Theorem      85
Gaussian      205 207 208 209 210 211 287
Gaussian distribution      64
Gaussian process      63
Gaussian product      112 124
Gaussian white noise      310
General method      213
Generalized random process      79
Gibbs — Liouville theory      97
Gram — Charlier series      281 284 285
Green’s function      1 3 4 5 6 7 8 9 11 14 16 18 22 27 28 37 41 43 45 46 47 48 51 52 54 56 102 127 142 145 148 221 225 226 244 298 305 323
Green’s function method      4 111
Green’s identity      89
Green’s matrix      111 311
Green’s Theorem      226
Heaviside step function      11
Helmholtz equation      323
Hermite polynomials      283 286 287
Hermitian positive definite function      76
Hierarchy method      103 111 112 114 115 117
Higher moments      67
Hilbert space      300
Independent process      63
INDEX      217
Index space      62
Initial condition      51 97 163
Input-output point of view      243
Integral kernel      115
Integration      74 92
Internal waves      83 221
Inverse method      201 202 203 204
Inverse operator      134 135 213 226 262
Inverse operator method      170 183 186
Invertible deterministic operator      97
Iterative solution      119
Ito equation      243 245 246 247
Ito form      245
Joint moment      64
Jointly stationary of order n      278
Karhunen — Loeve expansion      75 76 246
Kernel      93
Kolmogorov’s diffusion process      243
Kronecker delta      49 139
Lagrange’s equations of motion      97
Langevin’s equation      98
Laplace transform      82 84
Laplacian operator      48
Lebesgue integral      20
Linear      2 3
Linear operator      109
Linear stochastic operator      191
Linearization      269
Lipschitz condition      238 245
Local independence      113
ltd integral      244
Maclaurin series      287
Markov process      63
Markov theorem      78
Matrix differential equation      307
Mean square deviation      68
Measure equation      315

Multi-input-multi-output system      41
Neuman series      309 310
Newton’s law problem      28
Nonlinear      1
Nonlinear operator      82 181
Nonlinear partial differential equation      283
Nonlinear stochastic differential equation      152 238 239 296
Nonlinear stochastic operator      83 245
Nonlinear stochastic system      174 190
Nonlinear stochastic volterra equation      162
Nonlinear Volterra Equation      156
Nonstationary process      65
Numerical comparisons      205
Operator identity      134 136
Operator-theoretic approach      268
Operator-theoretic solution      174
Optimal correction      190
Order of approximation      173
Ornstein — Uhlenbeck process      64 117 205 318 321
Parametrized decomposition      163
Perturbation      159 208
Perturbation limit      247
Perturbation theory      103 104 109 112 113 115 118 255
Perturbative treatment      209
Picard’s method of successive approximations      230 231 233 238 241 242
Polynomial nonlinearities      165
probability density      59 242 297
Probability density function      61 280
Probability measure      59
Probability space      60
Probability theory      59
Product nonlinearities      183
Quadratic nonlinearity      162 168
Quadrature method      209
Quantum-mechanical many-body problem      114
Quasimoments      286 289 291
Quasimonochromaticity      269
Random experiment      59
Random field      72
Random function      59 60 66 67 68 75 79 82 88
Random Green’s functions      85 137 251 255
Random harmonic oscillator      318
Random initial conditions      138 141 162
Random operator      105
Random process      78 79
Random sampling operator      93
Random variable      59 60
Random walk      61
Random wave propagation      323
Randomness      2
realizations      60
Resolvent kernel      133 137 253 308 313
Riccati equation      229 305 307
Riemann integral      20
Riemann — Stieltje’s integral      245
Runge — Kutta methods      207
Sample function      60
Sample space      59
Scalar random funct ion      108
Schmidt orthogonalization      77
Schwartz distributions      6
Second-order improvement      189 200
Second-stage approximation      202
Separability      115 309
Sequence of values      275
Sigma field      54
Signal processing      316
Simple nonlinear operators      215
Simulation      207 213
Single-input-single-output (s.i.s.o.) systems      36
Spectral density      70
Spectral distribution function      70
Spectral spreading      269 323
State equation      315
State space      62
State space equation      310
Stationarity      70 124 247
Stationarity concepts      276
Stationary      70
Stationary process      65 70
Statistical independence      275
Statistical measure      58 66 84 88 164 199 213 263 265 272 298 300 303 308
Statistical mechanics      97
Statistical operator      88
Statistical separation      310
Statistically independent of order n      275
Stieltje’s integral      66
Stochastic      1
Stochastic bilinear concomitant      53 89 90 92 98 102 120 138 141 149 154 155 162 306
Stochastic calculus      243
Stochastic control      310
Stochastic control system      314
Stochastic differential equation      2 83 96 97 148 225 243 244 292
Stochastic differential operator      90 96
Stochastic dynamical system      243
Stochastic filter      83 84 244
Stochastic Green’s formula      120 125 138 155
Stochastic Green’s functions      84 86 115 124 129 130 137 243 244 245 247 250 251 253 255 256 264 265 298 308 313 314 315
Stochastic Green’s theorem      89 92 101 305
Stochastic matrix      310
Stochastic metric      278
Stochastic nonlinear inverse      268
Stochastic operator      82 83 85 86 99 243 244 264 265 271 298 303
Stochastic operator theory      1
Stochastic partial differential equation      257 260 263
Stochastic process      2 58 59 60 61 66 73 246 272
Stochastic Riccati equation      305
Stochastic systems      82 98 265 294 307 308 316
Stochastic systems theory      230 238
Stochastic transformation      78 93
Stochastic transport equation      322
Stochastic Volterra equation      103 104 119 120 133 134
Stochastic Volterra integral equation      120 309
Stochasticity      2 58 148 225 227 268 285
Strictly stationary of order h      277
Sturm — Liouville equation      7 8 9 11 13 15 31 32 42 45 46
Sturm — Liouville equation (homogeneous)      11
Sturm — Liouville operator      7 9 27 30 32 45
Successive improvements      186
Sum decomposition      220
Superposition      3
Symbolic function      24 25
Symmetric method      202 203 204
Symmetrized form      161—162
Symmetrized method      183 201
Symmetrized solutions      161
Symmetry condition      62
System operator      6
Systems theory      1
Taylor expansion      204
Third-stage approximation      202
Time average      67
Time-invariant system      5 6
Trajectory      60
Turbulence      83 268
Uncorrelated random variables      246
Uniqueness      230 303
Variance      68
Volterra integral equation      100 101 102 245
Volterra series      309
White noise      64 79 205 243 246
Wiener process      244 245
Wiener — Khinchine theorem      70
wronskian      9 10 12 14 18 21 32 33 35 44 47 143 146

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