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| Emanuel Parzen — Stochastic processes (Classics in Applied Mathematics) |
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| Предметный указатель |
Random walk, positive recurrent 245 253 254 259 280
Random walk, properties of 258 259
Random walk, recurrent 225 236 244 259
Random walk, with absorbing barrier 231
Random walk, with reflecting barrier 231
Rayleigh distribution 25
Realization of a stochastic process see “Sample function”
Recurrence criterion 225 235
Recurrence time 265—268
Recurrence time, mean 242—247 252—255 267 268
Recurrent class 221—227 235
Recurrent Markov chain see “Markov chain irreducible recurrent”
Recurrent state 221—229 235 245—247 252 253 263 264 267 268
Recurrent state, definition of 221
Recurrent state, null 245
Recurrent state, positive 245 253
Recursive relations 195 200 201
Reflecting barrier 231
Regression analysis 114
Reliability, system 38 94 293
Renewal counting process 162 164 168 170 176 178 186 270
Renewal counting process, asymptotic normality of 180 181
Renewal counting process, definition of 160
Renewal counting process, delayed 162 163 178 179
Renewal counting process, is particle counter problems 162—168 179
Renewal counting process, mean value function of 170 171 174 178—181 183 186
Renewal counting process, moments of 179
Renewal counting process, sample function of 160 161
Renewal counting process, with exponential inter-arrival times 118 163 174 176
Renewal counting process, with gamma distributed inter-arrival times 176—177 181
Renewal equation 170—172 178 183
Renewal equation, solution of 173 179 184 186
Renewal theorem, key 183 184 186
Renyi, A. 40
Response function, frequency 105—108 110—113
Response function, impulse 105 113 156
Response function, of a filtered Poisson process 145—147
Return state 208 209 256
Reuter, G.E.H. 299
Rice, S.O. 150
Root, W.L. 31 160
Rosenblatt, M. 6
Rubin, H. 136
Sample averages 72—74
Sample covariance function 109
Sample description space 8 9 45
Sample function 72 74 86
Sample function, definition of 24
Sample function, of a Poisson process 29
Sample function, of a random telegraph signal 36
Sample function, of a renewal counting process 160 161
Sample function, of covariance stationary processes 108
Sample mean, ergodic 73—75
Sample mean, mean and variance of 82 86
Sample mean, of a continuous parameter stochastic process 75 76 78
Sample spectral density function 109 116
Satterthwaite, F.E. 57
Scaling circuits 162 185
Scarf, H. 4 179
Schottky, W. 1
Schwarz's inequality 75
Scintillation- counter see “Counter non-paralyzable”
Scott, E.L. 1 71 130
Second moment function 179
Second order stationary process see “Covariance stationary process”
Semi-conductor noise 38 293
Service times 82 148 149 190
Service times, of a finite-server queue 281—283 286 287
Service times, of a single-server queue 206 258 265
Service times, of an infinite-server queue 147
Service times, of queues 5 199
Sevastyanov, B.A. 283
Shot noise 2 7 31
Shot noise process 115 149 150
Shot noise, as a filtered Poisson process 144
Shot noise, as white noise 115
Shot noise, non-stationary 157
Sine wave 76 115
Sitgreaves, R. 136
Skellam, J.G. 32
Slepian, D. 40
Smith, W.L. 179 181 182 183
Smoluchowski, M.v. 1
Snell, J.L. 241
Spatial distribution of plants and animal communities 2 32 48
Spectral analysis 111
Spectral density function 110—116
Spectral density function, sample 109 116
Spectral distribution function 110
Spectrum see also “Spectral density function” 103 104 111
Stable characteristic function 151
Standard deviation, definition of 11
Standardized random variable, definition of 97 98
State space, decomposition of 209—211
State space, definition of 188
Stationary distribution, determination of 265
Stationary distribution, existence of 249—252 258 277
Stationary distribution, for queues 283 284 287
Stationary distribution, of a Markov chain, definition of 248 265
Stationary distribution, of a random walk 254
Stationary independent increments, of a compound Poisson process 99 130
Stationary independent increments, of a generalized Poisson process 126
Stationary independent increments, of a Poisson process 30
Stationary independent increments, of a Wiener process 28
Stationary independent increments, stochastic processes with see also “Poisson process generalized” 33 35 77 121
Stationary independent increments, stochastic processes with, asymptotic normality of 103
Stationary independent increments, stochastic processes with, characteristic function of 123 124
Stationary independent increments, stochastic processes with, definition of 27
Stationary Markov chain see “Markov chain homogeneous”
Stationary process 69 72 113 114
Stationary process, covariance see “Covariance stationary process”
Stationary process, Markov process with 189
Stationary process, strictly 70—73 77 249
Stationary transition probabilities, Markov chain with see “Markov chain homogeneous”
Statistical communication theory 1 2 84 103 104 109 197 198
| Statistical decision theory 43
Statistical mechanics 1 2 27 73
Statistical spectral analysis 111
Steady state 189
Steffensen, J.F. 201
Stieltjes integral 42
Stirling's formula 225
Stochastic differential equations 84 113
Stochastic integral 79 80 295
Stochastic integral, notion of 39 76 79 80
Stochastic processes, approximately normal 98 101
Stochastic processes, classification of 7 8
Stochastic processes, continuous parameter see “Continuous parameter process”
Stochastic processes, covariance stationary see “Covariance stationary process”
Stochastic processes, definition of 6 7 22—24
Stochastic processes, derivative of 83 84 87
Stochastic processes, discrete parameter see “Discrete parameter process”
Stochastic processes, ergodic 74 75
Stochastic processes, evolutionary 69
Stochastic processes, identically distributed 25
Stochastic processes, independence of 25
Stochastic processes, integer-valued 117 123 160 299
Stochastic processes, stationary 69 72 113 114
Stochastic processes, strictly stationary 70—73 77 249
Stochastic processes, two-valued 36 38 40
Success runs 237
Syski, R. 4 299 302
System failures see “Failures system”
System reliability 38 94 293
Takacs, L. 182 183
Telegraph signal, random 37
ter Haar, D. 73
Testing hypotheses 3 135 137 139 142—144
Thermal noise 2 7 27
Thief of Baghdad problem 50
Time before absorption 238
Time series 71 111 114
Time series analysis 1
Time series, definition of 5
Time series, economic 6
Time to absorption 238—246 263
Time-of-delivery lag 4
Transient state see “Non-recurrent state”
Transition intensity 289 293
Transition intensity, definition of 277 278
Transition intensity, of a birth and death process 281—283
Transition probability function 289 196 198 213 221 238 265 277 278
Transition probability function, asymptotic behavior of 247 272
Transition probability function, definition of 188 193 194
Transition probability function, determination of 195
Transition probability function, differential equations for 289 291—293 295
Transition probability function, in the Chapman — Kolmogorov equation 203 276 300
Transition probability function, limit theorems for 219
Transition probability function, of a birth and death process 278 283 299 300 306
Transition probability function, of a branching process 200 201
Transition probability function, of a finite Markov chain 196 197
Transition probability function, of a pure birth process 295 296
Transition probability function, of a pure death process 299
Transition probability function, one-step 193 200 207 277
Transition probability generating function 300—306
Transition probability matrix 196 225 235 237 243 263 270
Transition probability matrix, definition of 194
Transition probability matrix, doubly stochastic 255 256 262
Transition probability matrix, estimation of 207
Transition probability matrix, in the Chapman — Kolmogorov equation 195
Transition probability matrix, of a finite absorbing Markov chain 246
Transition probability matrix, of a finite Markov chain 196 211 241 257 258
Transition probability matrix, of a finite random walk 232 233 242
Transition probability matrix, of a homogeneous Markov chain 196—198 204 206 207
Transition probability matrix, of a random walk 230 236 243—245 253 259 280
Transition probability matrix, of a two-state Markov chain 197 198 207
Truncated Poisson process 298
Two-state Markov chain 197 207 213 293 256
Two-valued process 36 38 40
Type I counter 164
Type II counter 158 164—166 181 182 186
Uhlenbeck, G.E. 97
Uncorrelated random variables, definition of 16
Uniform distribution 14 21 76 77 100 132
Uniform distribution, and the Poisson distribution 140 141 143 154 158
Vacuum tube 2 30 31 150
Variance, definition of 11
Variances, table of 13 14
von Neumann, J. 73
Waiting times 5 50 132 133 138
Waiting times, and order statistics 140 143
Waiting times, in Markov chains 265—269
Waiting times, in queues 283 285—287
Waiting times, in renewal processes 166 174 175 178
Wax, N. 27
Weakly stationary process see “Covariance stationary process”
Weibull distribution 169
White noise 113—115
Whittle, P. 85
Wide-sense stationary process see “Covariance stationary process”
Wiener process 8 26—29 40
Wiener process, and the Ornstein — Uhlenbeck process 97
Wiener process, as a martingale 65
Wiener process, as a model for Brownian motion 27 98 99 129
Wiener process, as a normal process 88 91
Wiener process, covariance kernel of 67 68 76
Wiener process, definition of 28
Wiener process, in goodness of fit tests 99—103
Wiener process, integrated 81 87
Wiener process, mean value function of 67 76
Wiener process, processes related to 95 96 102 103
Wiener — Khintchine relations 110
Wiener, N. 28 29 108 110
Wold, H. 6
Wonham, W.M. 37
Wynn, A.H.A. 102 137 139
Yule process 297
Yule, G.U. 57 297—298
Zero crossing problem 40
Zero-one law 215
Zero-one process see also “Twovalued process” 38 39
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