Author | Anderson, William J. author |
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Title | Continuous-Time Markov Chains [electronic resource] : An Applications-Oriented Approach / by William J. Anderson |
Imprint | New York, NY : Springer New York, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3038-0 |
Descript | XII, 355 p. online resource |
1 Transition Functions and Resolvents -- 1. Markov Chains and Transition Functions: Definitions and Basic Properties -- 2. Differentiability Properties of Transition Functions and Significance of the Q-Matrix -- 3. Resolvent Functions and Their Properties -- 4. The Functional-Analytic Setting for Transition Functions and Resolvents -- 5. Feller Transition Functions -- 6. Kendallโs Representation of Reversible Transition Functions -- 7. Appendix -- 2 Existence and Uniqueness of Q-Functions -- 1. Q-Functions and the Kolmogorov Backward and Forward Equations -- 2. Existence and Uniqueness of Q-Functions -- 3 Examples of Continuous-Time Markov Chains -- 1. Finite Markov Chains -- 2. Birth and Death Processes -- 3. Continuous Time Parameter Markov Branching Processes -- 4 More on the Uniqueness Problem -- 1. Laplace Transform Tools -- 2. Non-uniquenessโConstruction of Q-Functions Other Than the Minimal One -- 3. UniquenessโThe Non-Conservative Case -- 5 Classification of States and Invariant Measures -- 1. Classification of States -- 2. Sub-invariant and Invariant Measures -- 3. Classification Based on the Q-Matrix -- 4. Determination of Invariant Measures from the Q-Matrix -- 6 Strong and Exponential Ergodicity -- 1. The Ergodic Coefficient and Hitting Times -- 2. Ordinary Ergodicity -- 3. Strong Ergodicity -- 4. Geometric Ergodicity for Discrete Time Chains -- 5. The Croft-Kingman Lemmas -- 6. Exponential Ergodicity for Continuous-Time Chains -- 7 Reversibility, Monotonicity, and Other Properties -- 1. Symmetry and Reversibility -- 2. Exponential Families of Transition Functions -- 3. Stochastic Monotonicity and Comparability -- 4. Dual Processes -- 5. Coupling -- 8 Birth and Death Processes -- 1. The Potential Coefficients and Fellerโs Boundary Conditions -- 2. Karlin and McGregorโs Representation Theorem and Duality -- 3. The Stieltjes Moment Problem -- 4. The Karlin-McGregor Method of Solution -- 5. Total Positivity of the Birth and Death Transition Function -- 9 Population Processes -- 1. Upwardly Skip-Free Processes -- 2. Extinction Times and Probability of Extinction for Upwardly Skip-Free Processes -- 3. Multidimensional Population Processes -- 4. Two-Dimensional Competition Processes -- 5. Birth, Death, and Migration Processes -- Symbol Index -- Author Index