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Loeve M. — Probability Theory (part 2)
Loeve M. — Probability Theory (part 2)



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Название: Probability Theory (part 2)

Автор: Loeve M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 413

Добавлена в каталог: 19.05.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\Phi$-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 $\sigma$-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, $\sigma$-additive      83 111
Set function, $\sigma$-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, $C_o$      347
Space, $C_u$      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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