Thorisson H. — Coupling, Stationarity, and Regeneration :: Электронная библиотека попечительского совета мехмата МГУ

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Thorisson H. — Coupling, Stationarity, and Regeneration

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Название: Coupling, Stationarity, and Regeneration

Автор: Thorisson H.

Аннотация:

This is a book on coupling, including self-contained treatments of stationarity and regeneration. Coupling is the central topic in the first half of the book, and then enters as a tool in the latter half. The ten chapters are grouped into four parts.

Язык:

Рубрика: Социология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 517

Добавлена в каталог: 02.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\mathcal{A}$ -coupling event      149
$\mathcal{A}$ -identical      149
$\sigma$ -algebra, exchangeable      243
$\sigma$ -algebra, generated by      78 79
$\sigma$ -algebra, induced by      78 79
$\sigma$ -algebra, invariant      161 174 221 232
$\sigma$ -algebra, post-t      153
$\sigma$ -algebra, remote      247
$\sigma$ -algebra, smooth tail      161 188
$\sigma$ -algebra, tail      156 161 246
$\sigma$ -algebra, trivial      196
$\sigma$ -finite      214
$\varepsilon$ -coupling      178 (see also “Epsilon-couplings)
$\varepsilon$ -coupling, distributional      179
$\varepsilon$ -coupling, inequality      181
$\varepsilon$ -coupling, maximality      187
$\varepsilon$ -coupling, nondistributional      179
$\varepsilon$ -coupling, successful      72
Absolutely continuous      82
Age process      69 339
Almost sure (a.s.)      81 87
Aperiodic      42 47 344
Aperiodic strongly      47
Bell inequality      27 479
Biasing, exponential-biasing      442
Biasing, length-biasing      70 250 259 284 341 345
Biasing, length-debiasing      250 259 284
Biasing, volume-biasing      310 323
Biasing, volume-debiasing      316
Birth and death process      33
Borel, equivalence      88
Borel, equivalent, isomorphic      88
Borel, set      78
Brownian motion      97 128 242 336
Can be close to      57
Canonical      78
Cartesian product      79
Cemetery      132
Censoring state      132
Classical coupling      34 385 399
Common probability space      81
Complete metric space      86
Component      94
Component, common component      104
condition in      88
Conditional distribution      87
Conditional distribution, regular      88
Conditional distribution, version of      87
Conditional distribution, weak-sense-regular      135
Conditional expectation      87
Conditional independence      87 90 91
Conditional probability      87
Conditionally i.i.d.      91
Convergence      35
Convergence from-the-past      338 422
Convergence in distribution      23 118 184 185 269
Convergence in the path space      183—185
Convergence in the state space      183—185 195
Convergence rate      409
Convergence rate, exponential order $\rho$       144
Convergence rate, geometric order $\rho$       144
Convergence rate, moment-order $\dot{\varphi}$       145
Convergence rate, order $\varphi$       144
Convergence rate, power moment-order $\alpha - 1$       168
Convergence rate, power order $\alpha$       144 168
Convergence rate, uniform      406
Convergence to-the-future      338 422
Convergence, Cesaro total variation      161 167 288 331 345
Convergence, dominated      26
Convergence, geometric rate      46
Convergence, plain total variation      143 266 351 361 378
Convergence, pointwise      21 118
Convergence, smooth total variation      161 182 267 354 362
Convergence, taboo limit      436
Convergence, time-average total variation      167
Convergence, uniform      46 146 168 183 401
Convergence, weakly      118
Copy      1 78
Coupling      1 79 125 161 “Epsilon “Exact “Shift “Transformation
Coupling, canonical version      80
Coupling, classical      34 338
Coupling, decoupling      484
Coupling, distributional      140 142
Coupling, epoch      34 137
Coupling, event      7 106
Coupling, event inequality      7 9 14 112 141
Coupling, from-the-past      338 428
Coupling, i.i.d.      2
Coupling, impossible      27 479
Coupling, independence      2 79
Coupling, index      113 115 116
Coupling, index inequality      113 115 116
Coupling, indicator      106
Coupling, maximal      7 9 10 106 141
Coupling, maximal w.r.t. A      151
Coupling, Ornstein      48
Coupling, permutation      243
Coupling, quantile      3
Coupling, radius inequality      247
Coupling, regenerative processes      349 376
Coupling, remote      247
Coupling, rotation      243
Coupling, self-      2
Coupling, site inequality      246
Coupling, strong stationary time      481
Coupling, successful      35
Coupling, time      34 137
Coupling, time inequality      35
CYCLE      53 252 340 438
Cycle, one-dependent cycles      366
Cycle-length      252 340 438
Cycle-stationary      249 250 254 259 284 295 341
Defined on      78
Delay      53 340 438
Delay time      62
Delay-length      341
Deleting a null event      82
Deleting an inner null set      82 84
Depends on ... only through      91
Diagonal      44
distribution      78
Distribution, initial      34
Distribution, joint      80
Distribution, marginal      79
Distribution, stationary      37
Distributionally unique      118
Domination in distribution      4
Domination, pointwise      4
Domination, stochastic      4 146 168 183 401
Drift      67
EPR      27 479
Epsilon-couplings      125 161 178
Epsilon-couplings, maximally successful      192
Epsilon-couplings, regeneration      354 362
Epsilon-couplings, success probability      178
Epsilon-couplings, successful      178
Event      81
Event, coupling      7
Event, coupling event      106
Event, null      81
Event, shift-coupling      219
Exact coupling      125 137 161
Exact coupling, coupling epoch      137
Exact coupling, coupling time      137
Exact coupling, coupling time inequality      35
Exact coupling, distributional      125 137
Exact coupling, maximal      147
Exact coupling, maximal at time t      146
Exact coupling, maximally successful      157
Exact coupling, random fields      245

Exact coupling, regeneration      351 361
Exact coupling, success probability      137
Exact coupling, successful      137
Exact coupling, time inequality      143
Exact coupling, time-inhomogeneous reg.      378
Exact transformation coupling      244
Exchangeability      243
Expectation, mean      86
Expectation, mean, conditional      87
Extension      80
Extension, conditioning      89
Extension, consistency      85
Extension, independence      85
Extension, product space      83
Extension, proper      83
Extension, reduction      82 84
Extension, splitting      94
Extension, transfer      92 135
F0lner averaging sets      220 227 240
Future-independent time      481
Generalized inverse      3
Greatest common divisor      42
Harmonic function      195
Harmonic function, harmonic      207
Harmonic function, smooth space-time      209
Harmonic function, smoothed version      209
Harmonic function, space-time harmonic      205
Harris chain      364
i.i.d. coupling      2
Independence coupling      2 79
Independent stationary background      302 305
Induced by      78
Initial position      47
Inspection paradox      70
Invariant $\sigma$ -algebra      161 174 221 232 281 320
Ionescu Tulcea theorem      89
Irreducible      33 39
Ising model      470
Jordan Hahn decomposition      112
Kolmogorov Extension Theorem      86
Lattice      57 343 351 361
Lebesgue interval      122
Lorentz transformations      244
Markov chain, continuous-time      39
Markov chain, coupling from-the-past      467
Markov chain, discrete-time      42
Markov chain, regular      45
Markov chain, simulation      467
Markov chain, time-homogeneous      39
Markov jump process      39
Markov process      201
Markov process, conditional stationary      214
Markov process, initial distribution      202
Markov process, regeneration set      364 365
Markov process, space-time process      375
Markov process, stationary distribution      213
Markov process, stationary measure      213
Markov process, strong      44 365
Markov process, taboo regenerative      440
Markov process, time-homogeneous      201
Markov process, transition probabilities      201
Markov process, uniform nullity      214
Markov process, version      202
Markov property      39
Markov property, strong      44 364
Maximal coupling      7 9 10
Maximal coupling event      7 9
Measure dependent      82
Measure-free      251
Mixing      195
Mixing, Cesaro mixing      199
Mixing, mixing      196 351 361 378
Mixing, smoothly mixing      200 354 362
Moment, $\alpha$ -moment      45 167
Moment, $\varphi$ -moment      144
Moment, classical coupling time      406 409
Mutually singular      107
Nonexplosion      33
Nonlattice      57 354 362
Nonlattice, strongly      61
Nonlocality      27 479
Ornstein coupling      48
Outcome      81
Palm theory      250
Palm theory, associated Z and S      253
Palm theory, coincidence of duals      290 335
Palm theory, cycle-stationary      254 259 284
Palm theory, duals      263
Palm theory, ergodic case      291
Palm theory, inversion formula      264
Palm theory, length-biasing      250 284
Palm theory, length-debiasing      250 284
Palm theory, Palm characterization      308 316
Palm theory, point process      293 296
Palm theory, point-at-zero duality      250 259 323
Palm theory, point-stationary      295 299 304 305 323
Palm theory, point/site      297
Palm theory, point/time      251
Palm theory, process and points      251
Palm theory, randomization      317
Palm theory, regenerative      262
Palm theory, sequence space $(L, \mathcal{L})$       251
Palm theory, stationary      254 259 284 295 298 304 323 337
Palm theory, version      263
Palm theory, volume-biasing      310 323
Palm theory, volume-debiasing      316 323
Palm theory, Voronoi cells      308
Part      94
Poincare transformations      244
Point of increase      57
Point-map      300
Point-map, extended      303
Point-shift      283 300
Point-shift, bijective      302 304
Point-shift, extended      304
Point-stationary      295 299 304 305 323
Point-stationary, Palm characterization      308
Point-stationary, randomization      317
Poisson process      299 376
Polish space      85
Post-t $\sigma$ -algebra      153
Power set      88
Probability, conditional      87
Probability, kernel      88
Probability, mass function      7
Product CT-algebra      79
Product probability space      85
Product space      79
Projection mapping      79
Quantile, coupling      3
Quantile, function      3
Quantum physics      27 479
Quasi-stationary      467
Queue GI/GI/I      347
Queue GI/GI/k      369 376
Queue M/GI/k      376
Random element      78
Random element, conditional      89
Random element, external      81
Random element, independent      85
Random element, orginal      81
Random element, transferred      92
Random field      218
Random field, exact coupling      245
Random field, random site      218
Random field, rotation invariant      244
Random field, shift-coupling      218 219
Random field, shift-map      218
Random field, site set      218
Random walk      47

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