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| Авторизация |
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| Skorokhod A.V., Prokhorov Y.V. (Ed) — Basic Principles and Applications of Probability Theory |
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| Предметный указатель |
Plato 13
Pointwise estimation 196
Poisson distribution 26 39
Poisson process 83
Poisson's theorem 26
Poisson, S. 26 39 83 85
Positive-definite function 45
Power 203
Predictable cr-algebra 107
Predictable process 108
Predictable sets 108
Predictable stopping time 106ff
Predictable stopping time, completely 106
Prediction 17 257ff
probability 7ff 30ff 6 73 77ff 93ff HOff 123ff 145ff 177ff 187ff 193ff 225 229 235ff 249ff 266 269 273
Probability space(s) 24 29 46 64 140
Probability space(s), family of 147
Probability, definition 13
Probability, geometrical 29
Probability, of type I, type II errors 202
Probability, transition 99 125 126 148ff 156ff 177 187 225 229 269
Process with independent increments 78 80 83 90 104 110 268
Process with independent increments, discrete 78
Product measures 86ff 91 206
Product of algebras 24
Progressive measurability 106
Prokhorov, Yu. V. 135ff
Purely discontinuous process 156 159
Radon measure 121
Radon — Nikodym theorem 15 32
Radon, J. 15 32 87 121
Random element(s) 34 38 49 57 120 121ff
Random element(s), distribution of 44
Random element(s), independent 53 57
Random experiment, lOff 38
Random field 42
Random function 17 42ff 93ff 100ff 116 259 272
Random function, Gaussian 44
Random function, measurable 47
Random function, regular 94
Random function, separable 94
Random mapping 38
Random measure 115ff
Random polygonal path 135
Random process see Stochastic process
Random sample 196 198
Random variable(s) 29ff 14 53 59ff 78 100 HOff 132 139 140 198 202 207 241ff 258 269
Random variable(s), discrete 30
Random variable(s), distribution of 30
Random variable(s), independent 59 60ff 78 132 140
Random vector 40ff 241
Random walk 67 7Iff 227 228
Random walk, arithmetic 71
Random walk, recurrent 71
Random walk, semibounded 77
Randomized strategy 217
Ratio theorem 127
Recurrency 74
Regular modification 94
Relative frequency 12ff 22 67 133 196ff
Renewal function 68
Renewal scheme 67
Renewal time 68
Riemann, B. 101ff
Risk function 208
Sample data 195ff 208
Sample distribution function 198
Sample mean 199 209
Sample moment 199
Sample points 11
Sample quantile 199
Sample space 11
Sample standard deviation 199
Sample variance 199
| Sampling 199
Sampling parameters 199
Sazonov, V.V. 51
Self-similar process 178
Semibounded walk 77
Semimartingale 111
Separable random functions 94
Sequential decision 211
Shannon's Theorem 249
Shannon, C. 249ff 273ff
Shifting operator 124 130
Sigma algebra 27
Sigma algebra, cylinder 48
Sigma algebra, predictable 107
Sigma algebra, tail 56
Signal detection 205
Smirnov, N.V. 200 201
Space of elementary events 11
Spectral density 260 265
Spectral function 259
State space 147
Stationary process 130 244 254
Stationary process, ergodic 130
Stationary sequence 125 130 131 239ff 259 264
Stationary sequence, ergodic 131
Stationary sequence, strict-sense 124
Stationary sequence, wide-sense 117 259
Statistic 196ff
Statistic, sufficient 196 198
Step-controls 228 230 233
Stirling's formula 26
Stirling, J. 26
Stochastic analysis 17
Stochastic equivalence 93
Stochastic integral 116 179 181
Stochastic interval 107
Stochastic process(es) 42 43 53 67 104 139 140 145 193 215
Stochastic process(es), consistent 49
Stochastic process(es), continuous 79
Stochastic process(es), controlled 193 215
Stochastically continuous process 80 83 99
Stopping time 105ff 170 211 225 227 267
Stopping time, predictable 106ff
Strategy 217 218 225 229 230
Subharmonic function 227
Submartingale 111ff 227
Sufficient statistic 196 198
Superharmonic function 226
Supermartingale 111ff
Symmetrization 64 82
Tail  -algebra 56
Tests of hypotheses 202ff
Three-series theorem 78 79
Tightness 121
Total probability formula 22
Transition probability 99 125 126 148ff 162 177 187 225 269
Transport coefficient (vector) 162 165
Type I, type II probability errors 202
Unbiased estimator 196ff
Uniform distribution 39 41
Uniform stochastic continuity 79
Uniform tightness 121
Uniformly integrable 37 91 114
Uniformly integrable, martingale 114
Uniprovable tests 204
Variance 31 40 60 85 87 91 132 133 162 196 199 200 206 209
Variational series 198
Weak compactness 122 136
Weak convergence 119
Weak distribution 50 52
Weak-continuity condition 220 224
Wiener measure 178
Wiener process 176ff
Wiener, N. 74 84 85 104 135 145 162 176ff 202 268ff
Yaglom, A.M. 262 274
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