Meyn S.P., Tweedie R.L. — Markov Chains and Stochastic Stability :: Электронная библиотека попечительского совета мехмата МГУ

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Meyn S.P., Tweedie R.L. — Markov Chains and Stochastic Stability

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Название: Markov Chains and Stochastic Stability

Авторы: Meyn S.P., Tweedie R.L.

Аннотация:

The area of Markov chain theory and application has matured over the past 20 years. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique which not only affects applications, but also the development of the theory itself. The impact of the theory on specific models is discussed in detail.

Язык:

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 558

Добавлена в каталог: 18.12.2004

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Предметный указатель

Evanescence      17 207
Evanescence for Feller chains      457
Exchange rate      4
Exogenous variables      37
Expectation      518
f-regularity      332 352
f-regularity, criterion for      338
f-total variation norm      330
Fatou’s Lemma      517
Feller property      128
Finiteness of moments      345
First entrance decomposition      176 180
First-entrance last-exit decomposition      312
Forward accessible      151 155
Forward recurrence time chains      44 60 236
Forward recurrence time chains, $\delta$ -skeleton      75 112 349
Forward recurrence time chains, Geo. ergodicity for      361
Forward recurrence time chains, positivity for      247
Forward recurrence time chains, recurrence for      177
Forward recurrence time chains, regularity for      271
Forward recurrence time chains, V-uniform ergodicity for      389
Forward recurrence time process      75
Foster — Lyapunov criteria      19
Foster’s criterion      262 284
Full set      89
Functional CLT      525
Functions unbounded off petite sets      191
Generalized sampling      289
Geometric Ergodic Theorem      354
Geometric ergodicity      354 360
Geometric ergodicity, drift criterion for      367
Geometrically ergodic atom      357 360
Globally attracting      160
Gumleaf attractor      34
Harmonic functions      414
Harris $\tau$ -property      497
Harris recurrence      200
Harris recurrence, topological of states      209
Harris, maximal set      205
Harris, positive      231
Increment (or disturbance)      24
Increment analysis      219
Increment analysis, geometric      397
Indecomposable      159
Independent and identically distributed      9
Indicator function      68 516
Inessential sets      199
Initial condition      55
Initial distribution      57
Innovation      24
Integrable functions      517
Invariant $\sigma$ -fields      412
Invariant events      414
Invariant measures      229
Invariant measures for e-chains      297
Invariant measures for Feller chains      287 295
Invariant measures for recurrent chains      241
Invariant measures, structure of      245
Invariant random variables      412 414
Invariant set      157
Invasion/antibody model      471
Irreducibity      83
Irreducibity, maximal measure      89
Irreducibity, open set      131 133
J, interarrival times for a dam      49 52
Kac’s Theorem      236
Kaplan’s condition      491
Kendall sets      364
Kendall’s Theorem      358
Kernel      65
Kernel, n-step transition probability      67
Kernel, Substochastic      77
Kernel, Transition probability      65
Kolmogorov’s inequality      524
L(x, h)      292
Ladder chains      76
Ladder chains, positivity for      248
Last-exit decomposition      180
Law of Large Numbers      410 413
Law of large numbers for e-chains      461
Law of large numbers, ratio form of the      417 424
Law of the iterated logarithm      411
LCM(F,G) model      9
Lebesgue integral      516
Lebesgue measure      516
Lindelof’s theorem      519
Linear control model      8 9 95
Linear control model, controllability for the      96
Linear state space models      9
Linear state space models as T-chains      138
Linear state space models, boundedness in prob. for      301
Linear state space models, central Limit Theorem for      443
Linear state space models, Gaussian      97 114
Linear state space models, positivity for      251
Linear state space models, simple      25
Linked forward recurrence time chains      237
Locally compact      519
Lower semicontinuous      126 520
M-irreducibity      160
Markov chain      3 58 66
Markov chain, definition of      55
Markov chain, time-homogeneous      58
Markov property      69
Markov property, strong      72
Markov transition function      65
Markov transition matrix      59
Martingale      524
Martingale difference sequence      524
Maximal Harris set      205
Maximal irreducibility measure      89
Mean drift      225
Mean square stabilizing      38
Measurable function      516
Measurable space      515
Measure      516
Metric space      519
Minimal set      158
Minimal subinvariant measures      243
Minimum variance control      38
Minorization Condition      102
Mixing      408
Mixing, V-geometric mixing      387
moment      228
Monotone Convergence Theorem      517
Moran dam      49 74
Multidimensional models      469
N(t), customers in queue at time t      45
Neighborhoods      519
networks      5 284
Noise      24
Non-evanescent      207 286 498
Nonlinear state space model      29 130 149
Nonlinear state space model, associated control system for      33
Nonlinear state space model, V-uniform ergodicity and      396
Norm, f      330
Norm, operator V-norm      385
Norm, total variation      310
Norm, V-norm      382
Norm-like functions      214 522
Norm-like sequence      476
NSS(F) model      32
Null chains      498
Null chains, -definition      498 500
Null chains, $\tau$ -definition      499
Null Markov process      230
Null sets      454
Null states      453 456
Occupation probabilities      461
Occupation time      70
Open sets      519

Orey’s Theorem      451
p(M), upper tail of renewal sequence      448
p(n), increment distribution of renewal sequence      43
P(x, A), one-step transition probability      58 66
Pakes’ lemma      283
Period      118
Persistence      199
Petite set      121
Phase-type service times      402
Poisson equation      431
Polling systems      401
Populations      5
Positive chain      230 498
Positive chain, -definition      498 500
Positive chain, $\tau$ -definition      499
Positive chain, T-chains      455
Positive sets      454
Positive state      447 453
Positive state, topologically      446
Precompact sets      519
Probability space      518
Process on A      244 253 294
Q(x, h)      292
Quasi-compact      407
Queues      4 45
Queues with re-entry      272
Queues, Geo. ergodicity for M/G/1      401
Queues, GI/G/1      47 76 111
Queues, GI/M/1      47 62 239
Queues, GI/M/1, positivity of the GI/M/1      240
Queues, GI/M/1, transience of the GI/M/1.      197
Queues, M/G/1      48 86
Queues, M/PH/1      402
Queues, phase type service and geo. ergodicity      402
Queues, polling systems and geo. ergodicity      401
Queues, positivity for M/G/1      237
Queues, Positivity for the GI/G/1      248 488
Q{A}, invariant random variable      414
R(x), emptying time for dam      51
Random coefficient autoregression      404
Random variable      518
Random walk      11 61 93 247
Random walk on half line      14 73 81 195 220
Random walk on half line, Bernoulli      178
Random walk on half line, Bernoulli, Geo. ergodicity of      379
Random walk, Central Limit Theorem for      442
Random walk, continuous components for      137
Random walk, f-regularity and ergodicity for      346
Random walk, recurrent      192
Random walk, regularity of      270
Random walk, simple      178
Random walk, transient      193
Random walk, V-uniform ergodicity of      389
Randomized first entrance times      289
Rate of convergence, exact      392
Rate of convergence, geometric      354
Ratio limit theorem      417
Reachable state      131 133 447 455
Real line      516
Recurrence      17
Recurrence, -definition      496
Recurrence, $\tau$ -definition      497
Recurrence, deterministic systems      260
Recurrent atom      175
Recurrent chain      176 182 496
Recurrent chain, structure of $\pi$ for      245
Recurrent set      173
Recurrent state      211
Regeneration times      43 105
Regenerative decomposition      320 356
Regenerative decomposition for geometrically regular chains      356
Regularity      255 333 498
Regularity and ergodicity      328
Regularity for Markov chains      498
Regularity for measures      519
Regularity for sets      255
Regularity for sets, f-geometrically regular sets      364
Regularity for sets, f-regular sets      333 339
Regularity, criterion for f-geometric regularity      367
Regularity, f-geometric      364 371
Renewal measure      75
Renewal process      43
Renewal process, delayed      74
Renewal process, recurrence for      177
Renewal Theorem      347
Renewal Theorem, Blackwell’s      348
Renewal Theorem, Kendall’s      358
Residual lifetime process      44
Resolvent equation      291
Resolvent kernel      68
Running maximum      425
Sample paths      55
Sampled chain      119
Sampled chain, generalized      289
Sampling distribution      119
Sampling, generalized      289
Semi-dynamical system      19 260
Separability      519
Sequence or path space      55
SETAR model      31 142 503
SETAR model, null recurrence      277
SETAR model, regularity      274
SETAR model, transience      222
Shift operator      69
Simple linear model      25
Simple linear model, regularity for the      271
Skeleton      68
Skip-free chain, invariant measure for      238
Skip-free random walk on a half line      197
Skip-free to the left, g      399
Skip-free to the right      77
Small set      106
SNSS(F) model      29
Splitting      102
Splitting a general Harris chains      422
Spread-out      111 247
Stability      15 173
Stability in the sense of Lyapunov      20
Stability, -properties and      496
Stability, $\tau$ -properties and      496
Stability, asymptotic      20
Stability, Drift properties and      496
Stability, global asymptotic      20
Stability, global exponential      302
Stability, Lagrange      20
Stability, Lagrange, for CM(F) model      396
State spaces      56
Stationary processes      230
Stochastic comparison      219
Stopping times      71
Stopping times, first hitting      70
Stopping times, first return      70
Storage model      4
Storage model, content-dependent      52
Storage model, simple      49 62
Strong Feller property      128
Strong Markov property      72
Strong mixing      383 387
Subinvariant measures      232
Sublevel set      190 520
Supermartingale      524
T(x,A), continuous component      127
T-chain      127 133
T-chain, bounded in probability      455
T-chain, positive recurrent      455
Taboo probabilities      73
Test function      501
Test set      501
The Martingale Convergence Theorem      524
Tight      17 285 521

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