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

Composition, lemma      227
Composition, theorem      206
Conditional characteristic function      25
Conditional distribution function      26
Conditional distribution, mixed      25
Conditional distributions existence theorem      27
Conditional expectation      24 4 6 7 8 10
Conditional independence      17 290
Conditional inequalities      14
Conditional median      51
Conditional probability      24 3 4 5 6 7
Conditional regular probability      138 19 20
Conditional uniform asymptotic negligibility      47
Consistency theorem      94
Consistent      93
Constant chain      29 32
Continuity condition      312
Continuity condition, uniform      317
Continuity extension theorem      177
Continuity in probability      167
Continuity in quadratic mean      135
Continuity in quadratic mean criterion      136
Continuity in r-th mean      167
Continuity lemma, $\Phi$ -weak      338
Continuity lemma, strong      336
Continuity lemma, uniform      180
Continuity of characteristic functions theorem      204 224
Continuity separation theorem      176
Continuity theorem(s) for additive set functions      85
Continuity theorem(s) for characteristic functions      204 224
Continuity theorem(s), sample      181
Continuity theorem(s), sample modulii      183
Continuity, $\sigma$ -uniform      318
Continuity, additive set functions—theorem      85
Continuity, equivalence lemma      223
Continuity, F- , interval      187
Continuity, modulus      264
Continuity, P- , set      189
Continuity, sample      167 188
Continuous, almost surely      167
Continuous, decomposability theorem      222
Continuous, decomposable normal      213
Continuous, decomposable Poisson      213
Continuous, decomposable process      212
Continuous, F-      187
Continuous, function      67
Continuous, functional      80
Continuous, P-      189
Continuous, set function      85
Continuous, stable process      372
Continuous, strongly      332
Contraction      333
Convergence criterion(ria) in quadratic mean      260 135
Convergence criterion(ria), almost everywhere      116
Convergence criterion(ria), almost sure      42
Convergence criterion(ria), central      323 327
Convergence criterion(ria), complete      204
Convergence criterion(ria), degenerate      290 329
Convergence criterion(ria), exponential      34
Convergence criterion(ria), iid      346
Convergence criterion(ria), iid, central      348
Convergence criterion(ria), normal      292 328
Convergence criterion(ria), Poisson      308 329
Convergence criterion(ria), Pr.'s on metric space      190
Convergence criterion(ria), weak      203
Convergence in measure      116
Convergence in quadratic mean      260 123 135
Convergence in r-th mean      159 14
Convergence lemma for semigroups      344
Convergence of sequences of sets      58
Convergence of series      248 214
Convergence of strong semi-groups      343
Convergence of types      216
Convergence theorem(s) of types      216
Convergence theorem(s), -      165
Convergence theorem(s), basic, almost sure      72
Convergence theorem(s), comparison      117
Convergence theorem(s), dominated      126
Convergence theorem(s), Fatou — Lebesgue      126
Convergence theorem(s), moments      186
Convergence theorem(s), monotone      125
Convergence theorem(s), submartingales      59
Convergence theorem(s), uniform      204
Convergence, $\Phi$ -weak      333
Convergence, almost everywhere      114
Convergence, almost sure      153
Convergence, almost uniform      140
Convergence, complete      180
Convergence, essential      262 214
Convergence, exponential      33
Convergence, H-type      349
Convergence, unconditional      215
Convergence, uniform      114
Convergence, weak      180 106
Convex functions      161
Correspondence lemma      344
Correspondence theorem      97
Countability lemma      168
Countable(ly)      16
Countable(ly) base      72
Countable(ly) class      57
Countable(ly) operations      57
Countable(ly) set      57
Countable(ly), valued      64 106
Covariance(s)      131
Covariance(s), closure theorem      134
Covariance(s), criterion      132
Covariance(s), harmonizable      140
Covariance(s), inversion of      141
Covariance(s), stationary      148
Covering open      69
Covering rule      16
Cramer      271 408 409 130 150 389
Crossings      57 202
Cylinder(s), Borel      62
Cylinder(s), product      62
Daly      410
Daniell      94 408
Decomposability, continuous-theorem      222
Decomposability, extension lemma      218
Decomposability, lemma      219
Decomposability, normal continuous-criteria      223
Decomposability, Poisson continuous-criteria      223
Decomposability, stationary derivatives-criterion      226
Decomposable laws, infinitely      308
Decomposable laws, self-      334
Decomposable process      212
Decomposable process, infinitely      213
Decomposable process, normal      213
Decomposable process, Poisson      213
Decomposition theorem(s), chains      37 94
Decomposition theorem(s), composition and-      283
Decomposition theorem(s), degenerate type      283
Decomposition theorem(s), distribution functions      178 200
Decomposition theorem(s), Hahn      87
Decomposition theorem(s), harmonic orthogonal      149
Decomposition theorem(s), integral      229
Decomposition theorem(s), Lebesgue      131
Decomposition theorem(s), normal type      283
Decomposition theorem(s), Poisson type      283
Decomposition theorem(s), proper orthogonal      144
Decomposition theorem(s), regular conditional probability      22
Decomposition theorem(s), second order integral      232
Decomposition theorem(s), three parts      216
Degenerate, characteristic functions      215
Degenerate, convergence criterion      290 329
Degenerate, distribution function      215
Degenerate, law      215
Degenerate, random time      376 189
Degenerate, random variable      215

Degenerate, random walk      370
Degenerate, type      215
Delteil      407
Dense set      72
Dense set, nowhere      75
Denumerable      16
Denumerable class      57
Denumerable set      57
Denumerable, set of operations      57
Denumerable, valued      64 106
Derivation of a q-pair      329
Diameter of a set      74
Dichotomy      380
Dichotomy criterion      382
Difference equations      48
Difference of sets      56
Difference, proper      56
Differentiation in quadratic mean      136
Differentiation in quadratic mean criterion      136
Differentiation lemma(s), $\Phi$ -weak      338
Differentiation lemma(s), point      252
Differentiation lemma(s), strong      337
Differentiation operator, $\Phi$ -weak      338
Differentiation operator, strong      337
Differentiation theorem for transition probabilities      317
Differentiation, strong      332
Diffusion operator(s), general      372
Diffusion operator(s), one-dimensional      374
Diffusion operator(s), theorem      373
Diffusion operator(s), theorem, one-dimensional      378
Direction(ted)      67
Direction(ted) set      68
Dirichlet      187
Discontinuity, first kind      167
Discontinuity, fixed      167
Discontinuity, jump      167
Discontinuity, moving      167
Discontinuity, simple      167
Discontinuous part, sample lemma      220
Disjoint class      57
Disjoint events      4
Disjoint sets      57
Distance of points      73
Distance of points and sets      78
Distance of sets      77
distribution      168 172 175
Distribution of particles, Poisson      234
Distribution, -      370
Distribution, conditional      25
Distribution, conditional, mixed      25
Distribution, conditional-existence theorem      27
Distribution, conditional-function      26
Distribution, empirical-function      20
Distribution, function      20 96 169 177
Distribution, initial      296
Distribution, invariant      39
Distribution, probability-      168
Doblin      30 302 354 403 411 117
Dobrushin      182 386
Domain      62 108
Domain of attraction      360
Domain, partial      401
Domain, standard      402
Dominated Convergence Theorem      126 72
Donsker      263 387
Donsker, invariance principle      271
Doob      26 54 57 77 91 161 166 193 288 312 385 386 387
Doubrovsky      407
Dowker      76 385
Duality rule      57
Dubins      384
Dugue      409
Dunford      76 99 384
Duration of stay      323 324
Dvoretsky, Erdoes and Kakutani      251 387
Dynkin      182 289 310 359 367 374 386 387
Egorov theorem      141
Einstein      43 44 235 387
Elementary chain      29 33
Elementary function      64 107
Elementary probability field      16
Elementary random variable      17 152
Elementary, Markov      302
Elementary, Markov—criterion      335
Empirical distribution function      20
Empty set      4 54
Endomorphism(s), $\Phi$ -adjoint      334
Equivalence class      36 154
Equivalence theorem(s)      263 379
Equivalence theorem(s), Markov      292
Equivalence theorem(s), strong Markov      309
Equivalence, Andersen      377 393
Equivalence, Andersen-lemma      378
Equivalence, convergence      245
Equivalence, lemma, continuity      221
Equivalence, lemma, laws      290
Equivalence, lemma, series      245
Equivalence, tail      245
Equivalence, weak      39
Equivalent, distribution function      96
Equivalent, functions      114
Equivalent, random functions      165
Equivalent, random variables      154
Equivalent, states      36
Erdoes      34 251
Erdoesand Kac      263
Ergodic criterion, -      105
Ergodic criterion, almost sure      101
Ergodic decomposition      90
Ergodic hypothesis      78 89
Ergodic inequality, basic      79 81
Ergodic method      77
Ergodic theorem(s)      77 79
Ergodic theorem(s), -      103
Ergodic theorem(s), almost sure      100
Ergodic theorem(s), basic      81
Ergodic theorem(s), norms      108 109
Ergodic theorem(s), uniform      113
Esseen      294 410
Essential convergence      262 214
Essential divergence      162
Euler      47
Events      3 8 151
Events, disjoint      3
Events, elementary      151
Events, exchangeable      45 51
Events, impossible      4 151
Events, independent      11 73 235
Events, invariant      79
Events, null      152
Events, random      5 8
Events, sure      4 151
Events, tail      241
Everreturn state      36
Exchangeable events      45 373
Exchangeable random variables      373 31 36
Expectation of a random function      156
Expectation of a random sequence      154
Expectation of a random variable      10 17 153 154
Expectation, centering at      244
Expectation, conditional      24 4 6 7 8 10
Expectation, indefinite      153
Exponential Bounds      266
Exponential convergence      33
Exponential convergence criterion      34
Exponential convergence theorem      35
Exponential identities      388 396
Extended Bernoulli law of large numbers      26
Extended Bienayme equality      52
Extended Borel line      93 107

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