Loeve M. — Probability Theory (part 2) :: Электронная библиотека попечительского совета мехмата МГУ

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Loeve M. — Probability Theory (part 2)

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Название: Probability Theory (part 2)

Автор: Loeve M.

Язык:

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

Предметный указатель

-invariance and continuity criterion      353
-inequality      157
-completeness theorem      163
-convergence theorem      164
-ergodic criteria      105
-space(s)      162
$\mathfrak{R}$ -definition      164
$\mu^o$ -measurable      88
$\sigma$ -additive      81 111
$\sigma$ -field(s)      59
$\sigma$ -field(s), chained      18
$\sigma$ -field(s), compound      156 235
$\sigma$ -field(s), independent      236
$\sigma$ -field(s), induced      64
$\sigma$ -field(s), invariant      79
$\sigma$ -field(s), minimal sufficient      13
$\sigma$ -field(s), product      61 62
$\sigma$ -field(s), separable      21
$\sigma$ -field(s), sufficient      11
$\sigma$ -field(s), tail      241
$\sigma$ -uniform continuity      318
(sub)Martingale(s)      54 55 194 195
(sub)Martingale(s) central lemma      200
(sub)Martingale(s) closure (sed)      54 200
(sub)Martingale(s) closure theorem      60
(sub)Martingale(s) convergence theorem      59
(sub)Martingale(s) criterion for Brownian motion      244
(sub)Martingale(s) crossings      57 202
(sub)Martingale(s) decomposition      55
(sub)Martingale(s) elementary closure properties      197
(sub)Martingale(s) elementary properties      195
(sub)Martingale(s) extension      206
(sub)Martingale(s) inequalities      57 201
(sub)Martingale(s) preserving transformations      196
(sub)Martingale(s) right closure lemma      197
(sub)Martingale(s) right regularization      206
(sub)Martingale(s) sample limits lemma      202
(sub)Martingale(s) sample limits theorem      203
(sub)Martingale(s) second order      129
(sub)Martingale(s) sequences      62
(sub)Martingale(s) stopping      208
(sub)Martingale(s) suprema theorem      199
(sub)Martingale(s), extended central lemma      208
(sub)Martingale(s), reversed sequences      62 63
(sub)Martingale(s), strong laws of large numbers      66
(sub)Martingale(s), supermartingale      195
(sub)Martingale(s), zero-one laws      64
Abel theorem      400
Absorbing state      314
Addition Property      10
Additive set function      82
Additive set function, $\sigma$ -additive      83 111
Additive set function, $\sigma$ -finite      83 111
Additive set function, continuity      85
Additive set function, continuity theorem      85
Additive set function, countably      83
Additive set function, decomposition      87
Additive set function, decomposition theorem      88
Additive set function, extension      88
Additive set function, extension theorem      88
Additive set function, finite      83 111
Additive set function, finitely      83
Additive set function, restriction      88
Adherence      66
Adherent point      66
Adjoint space      80
Adjoint, $\Phi$ -endomorphism      334
Alexandrov      190 409
Allard      44
Almost everywhere      112
Almost everywhere, Borel random function      169
Almost everywhere, convergence      114
Almost everywhere, mutual convergence      114
Almost sure(ly)      148
Almost sure(ly), continuous random function      167
Almost sure(ly), convergence      152 248 260
Almost sure(ly), equal random functions      165
Almost sure(ly), ergodic criterion      101
Almost sure(ly), ergodic theorem      100
Almost sure(ly), mutual convergence      153
Almost sure(ly), separability      173
Almost sure(ly), stability      244 249 274 260 124 52
Almost sure(ly), stability criterion      264
Andersen      368 379 404 411
Andersen and Jessen      92 408
Andersen equivalence      377 391
Andersen equivalence lemma      378
Andre, Desire      47 260
Araujo and Le Cam      287
Arcsine law      379 404 278
Arzela — Ascoli theorem      265
Asymptotic behaviour theorem      399
Asymptotic central problem      37
Asymptotic independence      42
Asymptotic passage theorem      36
Asymptotic uniform negligibility      302 47
atom      100 15 22
Attraction, domain of      360
Attraction, partial      403
Attraction, stability and criteria      364
Attraction, standard      402
Austin, Blumenthal and Chacon      387
Axioms of the countable case      16
Axioms of the finite case      8
Bachelier      212 236 386
Backward equation      311
Baire, category theorem      75
Baire, functions      109
Banach      407
Banach space      81
Banach, subspace, invariant      334
Base of a cylinder      62
Base of a linear subspace      126
Base, countable      72
Bawly      302 410
Baxter      369 390 411
Bayes theorem      24
bernoulli      407
Bernoulli case      12 244 280
Bernoulli, extended      26
Bernoulli, law of large numbers      14 244 282 11
Bernstein      407 289
Berry      294 410
Bienayme      408
Bienayme equality      12 246
Billingsley      196 409 264 382 386
Birkhoff      176 385
Birkhoff theorem      76 77
Blackwell      369 411 384
Blumenthal      361 383 386
Blumenthal, zero-one law      248
Bochner      408 409
Bochner theorem      220
Bogoliubov      110
Boltzmann statistics      42—43
Bolzano — Weirstrass property      70
Borel — Cantelli lemma      240
Borel(ian)      107 407 410
Borel(ian), cylinder      93
Borel(ian), field      93 104
Borel(ian), function      111 156
Borel(ian), line      93 107
Borel(ian), progressively—      192
Borel(ian), random function      168 169
Borel(ian), semi-groups      376
Borel(ian), sets      93 104
Borel(ian), space      93 107
Borel(ian), strong law of large numbers      18 19 26 244 11
Borel(ian), zero-one criterion      240
Bose — Einstein statistics      43—44

Bounded functional      80
Bounded Liapounov theorem      231 282
Bounded q-pair      329
Bounded set      74
Bounded totally      75
Bounded variances case      303
Bounded variances limit theorem      305
Bourbaki      407
Bray      409
Breiman      409 264 384
Breiman lemma      273
Brown(ian)      235
Brown(ian) asymptotic LIT      249
Brown(ian) Brown(ian) Laws of the iterated logarithm      249
Brown(ian) convergence criterion      269
Brown(ian) covariance criterion      238
Brown(ian) diffusion coefficient      237
Brown(ian) drift      237
Brown(ian) embedding lemma      272
Brown(ian) embedding theorem      273
Brown(ian) extrema      239
Brown(ian) extrema equalities      261
Brown(ian) extrema inequalities      243
Brown(ian) extrema laws      279
Brown(ian) first exit times      255
Brown(ian) hitting times      256
Brown(ian) invariance theorem      246
Brown(ian) level sets structure      259
Brown(ian) Lipschitz p-property      247
Brown(ian) local LIT      249
Brown(ian) martingales criterion for      244
Brown(ian) martingales property      239
Brown(ian) motion definition      244
Brown(ian) passage times      284
Brown(ian) process      223
Brown(ian) quadratic variation      253
Brown(ian) reflection principle      260
Brown(ian) sample continuity      243
Brown(ian) sample continuity modulus      247
Brown(ian) second order property      281
Brown(ian) times      254
Brown(ian) times origin invariance      258
Brown(ian) Wald relations      257
Brown(ian), distributed      238
Brown(ian), geometric      281
Brown(ian), reflected      281
Brunk      271 410
C-extension theorem      343
C-invariance and continuity criterion      352
Calculus, second order      135 137 185
Cantelli      20 240 409 410
Cantor theorem      74
Caratheodory extension theorem      88
Category theorem      75
Category, first      75
Category, second      75
Cauchy mutual convergence criterion      74 104 114
Centered sample lemma      218
Centering      244 81
Centering at expectations      244 51
Centering at medians      256 52
Centering function(s)      350 216
Centering lemma      216
Centering, unconditional      240
Central asymptotic problem      37
Central convergence criterion      323 326
Central inequalities      316
Central limit problem      302
Central limit theorem      321 322
Central statistical theorem      20
Chacon      384
Chain      29 31
Chain constant      29 32
Chain, elementary      29 33
Chain, quasi-strongly compact      115
Chain, second order      130
Chain, stationary      39 32
Chained $\sigma$ -fields      18
Chained classes      28
Chained events      28
Chained random variables      29 31
Change of variable lemma      190
Characteristic function(s)      198
Characteristic function(s) and dichotomy      386
Characteristic function(s), composition theorem      226
Characteristic function(s), conditional      26
Characteristic function(s), continuity theorem      204 224
Characteristic function(s), convergence criterion      204
Characteristic function(s), extension theorem      224
Characteristic function(s), general properties      207
Characteristic function(s), infinitely decomposable      306
Characteristic function(s), integral      202
Characteristic function(s), inversion formula      199
Characteristic function(s), self-decomposable      334
Characteristic function(s), stable      338 363
Characteristic function(s), triangular      386
Characteristic function(s), uniform convergence theorem      204
Chung      407 409 410
Chung and Fuchs      368 383 411
Chung and Ornstein      383 411
Class of sets      55
Class, closed under      59
Class, lower      272
Class, monotone      60
Class, upper      272
Classical degenerate convergence criterion      290
Classical limit problem      286
Classical normal convergence criterion      292
Closed class of states      36
Closed linear subspace      126
Closed model      22
Closed on the left (right) (sub)martingales      196
Closed set      66
Closed, strongly      107
Closed, under      59
Closed, weakly      107
Closure theorem(s), covariances      134
Closure theorem(s), infinitely decomposable laws      309
Closure theorem(s), submartingales      60
Cogburn and Tucker quadratic variation      283
Combinatorial lemma      378
Combinatorial method      47
Compact locally      71
Compact set      69
Compact space      69
Compact, strongly (quasi-)      107 110 115
Compact, weakly (quasi-)      107 110 115
Compactification      71
Compactness theorem for distribution functions      181
Compactness theorem for metric spaces      76
Compactness theorem for separated spaces      70
Compactness, properties      70
Compactness, relative      195
Compactness, relative—criterion      195
Comparison theorem for, convergences      117
Comparison theorem for, laws of sums      41
Comparison theorem for, lemma      303 320
Complement      4 56
Complete Complete convergence criterion      204
Complete convergence      180
Complete equivalence      39
Complete equivalence criterion      40
Complete measure      91
Complete metric space      74
Completeness theorem, -      163
Completion of $\sigma$ -fields      91
Completion of metric spaces      77
Complex random variable(s)      154 126
composition      204 283
Composition and decomposition theorem      283

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