دانلود کتاب Non-negative Matrices and Markov Chains

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Cover page......Page 1
Title page......Page 4
Preface......Page 7
Contents......Page 10
Glossary of Notation and Symbols......Page 13
PART I - FINITE NON-NEGATIVE MATRICES......Page 14
1.1 The Perron-Frobenius Theorem for Primitive Matrices......Page 16
1.2 Structure of a General Non-negative Matrix......Page 24
1.3 Irreducible Matrices......Page 31
1.4 Perron-Frobenius Theory for Irreducible Matrices......Page 35
Bibliography and Discussion......Page 38
Exercises......Page 39
2.1 The Equations: (sI - T)x = c......Page 43
Bibliography and Discussion to § 2.1......Page 51
Exercises on § 2.1......Page 52
2.2 Iterative Methods for Solution of Certain Linear Equation Systems......Page 54
Exercises on § 2.2......Page 57
2.3 Some Extensions of the Perron-Frobenius Structure......Page 58
Bibliography and Discussion to § 2.3......Page 66
Exercises on § 2.3......Page 67
2.4 Combinatorial Properties......Page 68
Exercises on § 2.4......Page 73
2.5 Spectrum Localization......Page 74
Bibliography and Discussion to § 2.5......Page 77
Exercises on § 2.5......Page 79
2.6 Estimating Non-negative Matrices from Marginal Totals......Page 80
Bibliography and Discussion to § 2.6......Page 88
Exercises on § 2.6......Page 92
3.1 Birkhoff\'s Contraction Coefficient: Generalities......Page 93
3.2 Results on Weak Ergodicity......Page 98
Bibliography and Discussion to §§ 3.1-3.2......Page 101
Exercises on §§ 3.1-3.2......Page 103
3.3 Strong Ergodicity for Forward Products......Page 105
Bibliography and Discussion to § 3.3......Page 112
3.4 Birkhoff\'s Contraction Coefficient: Derivation of Explicit Form......Page 113
Exercises on § 3.4......Page 124
CHAPTER 4 - Markov Chains and Finite Stochastic Matrices......Page 125
4.1 Markov Chains......Page 126
4.2 Finite Homogeneous Markov Chains......Page 131
Bibliography and Discussion to §§ 4.1-4.2......Page 144
Exercises on § 4.2......Page 145
4.3 Finite Inhomogeneous Markov Chains and Coefficients of Ergodicity......Page 147
4.4 Sufficient Conditions for Weak Ergodicity......Page 153
Bibliography and Discussion to §§ 4.3-4.4......Page 157
Exercises on §§ 4.3-4.4......Page 160
4.5 Strong Ergodicity for Forward Products......Page 162
Bibliography and Discussion to § 4.5......Page 164
Exercises on § 4.5......Page 165
4.6 Backwards Products......Page 166
Bibliography and Discussion to § 4.6......Page 170
Exercises on § 4.6......Page 171
PART II - COUNTABLE NON-NEGATIVE MATRICES......Page 172
5.1 Classification of Indices......Page 174
5.2 Limiting Behaviour for Recurrent Indices......Page 181
5.3 Irreducible Stochastic Matrices......Page 185
5.4 The \"Dual\" Approach; Subinvariant Vectors......Page
5.5 Potential and Boundary Theory for Transient Indices......Page 194
5.6 Example......Page 204
Bibliography and Discussion......Page 207
Exercises......Page 208
CHAPTER 6 - Countable Non-negative Matrices......Page 212
6.1 The Convergence Parameter R, and the R-Classification of T......Page 213
6.2 R-Subinvariance and Invariance; R-Positivity......Page 218
6.3 Consequences for Finite and Stochastic Infinite Matrices......Page 220
6.4 Finite Approximations to Infinite Irreducible T......Page 223
6.5 An Example......Page 228
Bibliography and Discussion......Page 231
Exercises......Page 232
CHAPTER 7 - Truncations of Infinite Stochastic Matrices......Page 234
7.1 Determinantal and Colactor Properties......Page 235
7.2 The Probability Algorithm......Page 242
7.3 Quasi-stationary Distributions......Page 249
Exercises......Page 255
APPENDICES......Page 258
Appendix A. Some Elementary Number Theory......Page 260
Appendix B. Some General Matrix Lemmas......Page 265
Appendix C. Upper Semi-continuous Functions......Page 268
Bibliography......Page 270
Author Index......Page 284
Subject Index......Page 288