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| Авторизация |
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| Loeve M. — Probability Theory (part 2) |
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| Предметный указатель |
Product, space 61 62
Prohorov 190 193 264 409 264 387
Projection 108
Projection theorem 127
Proper orthogonal decomposition 144
Proper subspace 108
Proper value 108
r-th in—mean 159
r-th, absolute moment 157 186
Rademacher inequality 123
Radon — Nikodym theorem 133
Radon — Nikodym theorem, extension 134
Raikov 283 411
Random analysis 163
Random event 5 8
Random function 152 156 163 164
Random function, Borel 168
Random function, decomposable 212
Random function, measurable 168
Random function, regular Markov 296
Random function, separable 171
Random function, stationary 169
Random function, theorem, stationarity 170
Random functions laws convergence criterion 268
Random process 164
Random sequence 152 155
Random stopping 208
Random time identities 390
Random time translations 376
Random time(s) 375 188 305
Random trial 6
Random variable 6 9 17 152
Random vector 152 155
Random walk 47 378 379
RANGE 63
Range space 62 105
Ranked random variables 350
Ranked sums 405
Ray 369 395 412
Real line 93
Real line, extended 93 107
Real number 93
Real number, extended 93
Recurrence criterion 32
Recurrence theorem 380
Recurrent state 31 380
Recurrent walk 380
Reflection principle 260
Regular conditional probability 138 19 20
Regular Markov existence theorem 297
Regular Markov process 294
Regular Markov random function 298
Regular process 164
Regular q-pair 329
Regular variation 354
Regular variation criterion 354
Regularity theorem 29
Relative compactness 190
Relative compactness theorem 195
Relative conditional expectation 10
Representation theorem 313
Representation theorem, integral 166
Reproducing kernel 156
Resolvent lemma 341
Resolvent lemma,  -weak 342
Restriced integration theorem 25
Return criterion 31
Return state 31
Riemann integral 129
Riemann — Stieltjes integral 128
Riemann — Stieltjes integralin quadratic mean 138
Riesz, F. 222 76
Riesz, F. lemma 81
Right regularization 206
Rightcontinuous process 370
Rightcontinuous stable processes extension lemma 371
Ruin, gambler's 48
Ryll — Nardzewski 77 385
Saks 408
Sample 167
Sample continuity 179
Sample continuity, Brownian 243
Sample continuity, moduli theorem 183
Sample continuity, modulus, Brownian 247
Sample, continuous 167
Sample, integrable 167
Sample, jumps lemma, Poisson 224
Sample, lemma, centered 218
Sample, lemma, discontinous part 220
Sample, limits lemma 361
Sample, measurable 167
Sample, probability space 168 29
Sample, rightcontinuity theorem, Markov 364
Sample, space 167
Sample, step functions theorem 329
Savage 374 411 11 384
Scalar product 80 122
Scheffe 408
Schwarz inequality 158
Second category 75
Second order calculus 185
Second order calculus theorem 186
Second order chain 130
Second order integral decomposition 232
Second order martingale 129
Second order random function 131
Second order random variable 121
Second order stationarity 148
Sections of functions 61 62 135
Sections of sets 61 62 135
Self-decomposable(bility) 334
Self-decomposable(bility) criterion 335
Semi-group(s), Borelian 336
Semi-group(s), convergence lemma 344
Semi-group(s), criterion, Markov 336
Semi-group(s), exponential 339
Semi-group(s), Markov 331
Semi-group(s), property 302 335
Semi-group(s), property, generalized 295
Semi-group(s), strongly convergent 343
Separability 170
Separability criteria 171
Separability existence theorem 173
Separability lemma 172
Separability, almost sure 173
Separable  -field 21
Separable random function 171
Separable space 72
Separating sets 171 174
Separation theorem, continuity 176
Sequences of laws, completely equivalent 39
Sequences of laws, weakly equivalent 39
Sequences, (sub)martingales 62
Sequences, convergence equivalent 245
Sequences, random 152 155
Sequences, reversed (sub)martingales 62 63
Sequences, stationary 83
Sequences, tail equivalent 245
Sequences, tail of 241
Series criterion, three 249
Series criterion, two 263
Set function, -additive 83 111
Set function, -finite 83 111
Set function, additive 83
Set function, continuous 85
Set function, countably additive 83
Set function, finite 82 111
Set function, finitely additive 83
Set(s), Borel 93 104
Set(s), bounded 74
| Set(s), closed 66
Set(s), compact 69
Set(s), dense 72
Set(s), directed 68
Set(s), empty 4 54
Set(s), Lebesgue 129
Set(s), measurable 60 64 107
Set(s), null 91 112
Set(s), open 66
Set(s), product 61
Set(s), separating 171 174
Set(s), subdirected 69
Set(s), totally bounded 75
Sevastianov 395
Shohat 187
Signed measure 87
Simple discontinuity 176 318
Simple function 64 107
Simple random variable 6 152
Skorohod 264 272 275 386
Skorohod, Brownian embedding 271
Skorohod, Gikhman and 386
Slutsky 130 386
Snell 384
Space of sets 55
Space,  347
Space,  347
Space, adjoint 81
Space, Banach 79
Space, Borel 93 107
Space, C 343
Space, compact 69
Space, complete metric 74
Space, D 275
Space, Hausdorff 68
Space, Hilbert 80
Space, induced probability 168
Space, linear 79
Space, measurable 60 64 107
Space, measure 112
Space, metric 173
Space, metric linear 79
Space, normal 78
Space, normed linear 79
Space, probability 91 151 152
Space, product 61 62
Space, product measurable 61 62 137
Space, product measure 136
Space, product probability 91
Space, range 62 105
Space, sample probability 168
Space, separated 68
Space, topological 66
Sphere 73
Spitzer 369 393 394 404 410 412
Spitzer, basic identity 396
Spitzer, basic theorem 401
Spitzer, Pollaczec—identity 393 400
Stability in probability 244 246
Stability in quadratic mean 122 124
Stability, almost sure 244
Stability, almost sure convergence and 124
Stability, almost sure criterion 264
Stability, and attraction criterion 364
Stability, normal—theorem 151
Stability, theorem 53
Stability, weak—including infinity 350
Stability, weak—uniform at infinity 353
Stable characteristic function 338
Stable law 338 363
Stable process 350
Stable process, continuous 372
Stable rightcontinuous extension lemma 371
State(s), absorbing 316
State(s), closed class of 36
State(s), equivalent 36
State(s), everreturn 36
State(s), indecomposable class of 36
State(s), instantaneous 316
State(s), nonrecurrent 31 380
State(s), noreturn 31
State(s), null 32
State(s), period of 33
State(s), positive 32
State(s), possible 370
State(s), recurrent 31
State(s), return 31
State(s), sets, uniformly continuous 314
State(s), space 165 289
State(s), steady 314
State(s), transient 380
Stationarity 301
Stationarity and law-derivatives 225
Stationarity inequalities 84
Stationarity integral 83
Stationarity integral—theorem 83 85
Stationarity lemma 84
Stationarity second order 148
Stationarity theorem 87
Stationarity theorem, random functions 170
Stationarity theorems, Markov 302 303
Stationary chain 39 33
Stationary covariance 148
Stationary decomposability criterion 226
Stationary Markov process 302 307
Stationary Markov time 307
Stationary process 225 303
Stationary random function 169 303
Stationary sequence 83
Stationary transition operator 302
Stationary transition probability 29 301
Steinhaus 409 411 384
Steinhaus, Banach- 102 332
Steinhaus, Kaczmarz and— 384
Step functions, sample—theorem 329
Stochastic independence 6 11
Stochastic process 164
Stochastic variable 174
Stone 131
stopping 208
Strisower 387
Strong closure 107
Strong continuity lemma 336
Strong convergence 106
Strong convergence in G 329 333
Strong differentiation lemma 337
Strong differentiation operator 337
Strong generator 337
Strong infinitesimal operator 337
Strong Kolmogorov equation 309
Strong laws of large numbers 66 233
Strong laws of large numbers, Borel 18 19 26 244 11
Strong laws of large numbers, Kolmogorov 241
Strong Markov equivalence theorem 309
Strong Markov property 304 308 357
Strong Markov property theorem 357
Strong normality 128
Strong resolvent 340
Strongly compact 107
Strongly continuous 332
Strongly convergent semi-groups 343
Strongly differentiable 332
Strongly integrable 332
Strongly normal 128
Strongly quasi-compact 110
Structure theorem 310
Submartingale see (sub) Mar ti ngale (s)
Subspace, closed linear 126
Subspace, invariant Banach 336
Subspace, linear 79
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