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Skorokhod A.V., Prokhorov Y.V. (Ed) — Basic Principles and Applications of Probability Theory
Skorokhod A.V., Prokhorov Y.V. (Ed) — Basic Principles and Applications of Probability Theory



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Название: Basic Principles and Applications of Probability Theory

Авторы: Skorokhod A.V., Prokhorov Y.V. (Ed)

Аннотация:

The book is an introduction to probability written by one of the famous experts in this area. Readers will learn about the basic concepts of probability and its applications, preparing them for more advanced and specialized works.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 260

Добавлена в каталог: 26.02.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\sigma$-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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