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xi | |
| Prologue to the second edition |
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xiii | |
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| Preface to the second |
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xvii | |
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| Preface to the first edition |
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xxi | |
|
I COMMUNICATION and REGENERATION |
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1 | (168) |
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3 | (18) |
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A range of Markovian environments |
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3 | (3) |
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6 | (7) |
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Stochastic stability for Markov models |
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13 | (6) |
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19 | (2) |
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21 | (27) |
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Markov models in time series |
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22 | (4) |
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Nonlinear state space models |
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26 | (7) |
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Models in control and systems theory |
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33 | (5) |
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Markov models with regeneration times |
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38 | (8) |
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46 | (2) |
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48 | (27) |
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Defining a Markovian process |
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49 | (2) |
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Foundations on a countable space |
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51 | (3) |
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Specific transition matrices |
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54 | (5) |
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Foundations for general state space chains |
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59 | (8) |
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Building transition kernels for specific models |
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67 | (5) |
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72 | (3) |
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75 | (21) |
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Communication and irreducibility: Countable spaces |
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76 | (5) |
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81 | (6) |
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Irreducibility for random walk models |
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87 | (2) |
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Irreducible linear models |
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89 | (4) |
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93 | (3) |
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96 | (27) |
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Splitting irreducible chains |
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97 | (5) |
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102 | (4) |
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Small sets for specific models |
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106 | (4) |
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110 | (5) |
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Petite sets and sampled chains |
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115 | (6) |
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121 | (2) |
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123 | (23) |
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Feller properties and forms of stability |
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125 | (5) |
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130 | (4) |
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Continuous components for specific models |
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134 | (5) |
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139 | (5) |
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144 | (2) |
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The nonlinear state space model |
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146 | (23) |
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Forward accessibility and continuous components |
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147 | (7) |
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Minimal sets and irreducibility |
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154 | (3) |
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Periodicity for nonlinear state space models |
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157 | (4) |
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Forward accessible examples |
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161 | (2) |
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Equicontinuity and the nonlinear state space model |
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163 | (2) |
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165 | (4) |
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169 | (142) |
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Transience and recurrence |
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171 | (28) |
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Classifying chains on countable spaces |
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173 | (4) |
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Classifying irreducible chains |
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177 | (5) |
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Recurrence and transience relationships |
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182 | (5) |
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Classification using drift criteria |
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187 | (6) |
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Classifying ranodom walk on R+ |
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193 | (4) |
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197 | (2) |
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Harris and topological recurrence |
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199 | (30) |
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201 | (5) |
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Non-evanescent and recurrent chains |
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206 | (2) |
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Topologically recurrent and transient states |
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208 | (5) |
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Criteria for stability on a topological space |
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213 | (5) |
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Stochastic comparison and increment analysis |
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218 | (10) |
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228 | (1) |
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229 | (27) |
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Stationarity and invariance |
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230 | (4) |
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The existence of π: chains with atoms |
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234 | (2) |
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Invariant measures for countable space models |
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236 | (5) |
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The existence of π: irreducible chains |
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241 | (6) |
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Invariant measures for general models |
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247 | (6) |
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253 | (3) |
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256 | (32) |
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258 | (3) |
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Drift, hitting times and deterministic models |
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261 | (2) |
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Dirft criteria for rugularity |
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263 | (9) |
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Using the resularity criteria |
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272 | (6) |
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Evaluating non-positivity |
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278 | (7) |
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285 | (3) |
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288 | (23) |
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Chains bounded in probability |
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289 | (3) |
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Generalized sampling and invariant measures |
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292 | (6) |
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The existence of a Q-finite invariant measure |
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298 | (2) |
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Invariant measures for e-chains |
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300 | (5) |
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Establishing boundedness in probability |
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305 | (3) |
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308 | (3) |
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311 | (218) |
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311 | (25) |
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Ergodic chains on countable spaces |
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316 | (4) |
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320 | (6) |
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Ergodicity of positive Harris chains |
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326 | (3) |
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Sums of transition probabilites |
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329 | (5) |
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334 | (2) |
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f-Ergodicity and f-regularity |
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336 | (26) |
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f-Properties: chains with atoms |
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338 | (4) |
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342 | (7) |
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f-Ergodicity for general chains |
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349 | (3) |
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f-Ergodicity of specific models |
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352 | (2) |
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354 | (5) |
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359 | (3) |
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362 | (30) |
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Geometric properties: chains with atoms |
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364 | (8) |
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Kendall sets and drift criteria |
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372 | (8) |
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f-Gemetric regularity of φ and its skeleton |
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380 | (8) |
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f-Geometric ergodicity for general chains |
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388 | (1) |
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Simple random walkand liner models |
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388 | (2) |
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390 | (2) |
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392 | (29) |
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OPerator norm convergence |
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395 | (5) |
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400 | (7) |
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Geometric ergodicity and increment analysis |
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407 | (4) |
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Models from queueing theory |
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411 | (3) |
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Autoregressive and state space models |
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414 | (4) |
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418 | (3) |
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Sample paths and limit theorems |
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421 | (41) |
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Invariant σ-field and the LLN |
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423 | (5) |
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Ergodic theorems for chains possessing an atom |
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428 | (5) |
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433 | (10) |
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443 | (7) |
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Criteria for the CLT and the LIL |
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450 | (4) |
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454 | (2) |
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456 | (6) |
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462 | (20) |
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464 | (5) |
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Characterizing positivity using Pn |
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469 | (2) |
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471 | (2) |
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473 | (4) |
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477 | (3) |
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480 | (2) |
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Generalized classification criteria |
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482 | (28) |
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483 | (8) |
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History-dependent drift criteria |
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491 | (7) |
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498 | (10) |
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508 | (2) |
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Epilogue to the second edition |
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510 | (19) |
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Geometric ergodicity and specral theroy |
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510 | (11) |
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521 | (2) |
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523 | (6) |
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529 | (38) |
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532 | (6) |
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Recurrence versus transience |
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532 | (2) |
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Positivity versus mullity |
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534 | (2) |
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536 | (2) |
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538 | (5) |
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Glossary of drift conditions |
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538 | (2) |
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The scalar SETAR model: a complete classification |
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540 | (3) |
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Glossary of model assumptions |
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543 | (9) |
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543 | (3) |
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546 | (6) |
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Some mathematical background |
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552 | (15) |
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552 | (3) |
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555 | (1) |
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556 | (1) |
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557 | (1) |
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Convergence concepts for measures |
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558 | (3) |
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561 | (2) |
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Some results on sequences and numbers |
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563 | (4) |
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567 | (20) |
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587 | |
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587 | |
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593 | |
Lisainfo e-raamatute kohta