Markov Chain Models - Rarity and Exponentiality - Livres de poche

EAN (ISBN-13): 9780387904054
ISBN (ISBN-10): 0387904050
Version reliée
Livre de poche
Date de parution: 1979
Editeur: SPRINGER VERLAG GMBH
208 Pages
Poids: 0,318 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2008-02-29T08:19:39+01:00 (Zurich)
Page de détail modifiée en dernier sur 2023-07-27T07:53:36+02:00 (Zurich)
ISBN/EAN: 0387904050

ISBN - Autres types d'écriture:
0-387-90405-0, 978-0-387-90405-4
Autres types d'écriture et termes associés:
Auteur du livre: keilson
Titre du livre: chain, markov chains, graduate text mathematics

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Données de l'éditeur

Auteur: J. Keilson
Titre: Applied Mathematical Sciences; Markov Chain Models — Rarity and Exponentiality
Editeur: Springer; Springer US
184 Pages
Date de parution: 1979-04-23
New York; NY; US
Langue: Anglais
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
XIV, 184 p.

BC; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Markov; Markov chain; Markowsche Kette; Random Walk; Sage; Variance; birth-death process; ergodicity; regenerative process; uniformization; Probability Theory; Stochastik; EA

0. Introduction and Summary.- 1. Discrete Time Markov Chains; Reversibility in Time.- §1.00. Introduction.- §1.0. Notation, Transition Laws.- §1.1. Irreducibility, Aperiodicity, Ergodicity; Stationary Chains.- §1.2. Approach to Ergodicity; Spectral Structure, Perron-Romanovsky-Frobenius Theorem.- §1.3. Time-Reversible Chains.- 2. Markov Chains in Continuous Time; Uniformization; Reversibility.- §2.00. Introduction.- §2.0. Notation, Transition Laws; A Review.- §2.1. Uniformizable Chains — A Bridge Between Discrete and Continuous Time Chains.- §2.2. Advantages and Prevalence of Uniformizable Chains.- §2.3. Ergodicity for Continuous Time Chains.- §2.4. Reversibility for Ergodic Markov Chains in Continuous Time.- §2.5. Prevalence of Time-Reversibility.- 3. More on Time-Reversibility; Potential Coefficients; Process Modification.- §3.00. Introduction.- §3.1. The Advantages of Time-Reversibility.- §3.2. The Spectral Representation.- §3.3. Potentials; Spectral Representation.- §3.4. More General Time-Reversible Chains.- §3.5. Process Modifications Preserving Reversibility.- §3.6. Replacement Processes.- 4. Potential Theory, Replacement, and Compensation.- §4.00. Introduction.- §4.1. The Green Potential.- §4.2. The Ergodic Distribution for a Replacement Process.- §4.3. The Compensation Method.- §4.4. Notation for the Homogeneous Random Walk.- §4.5. The Compensation Method Applied to the Homogeneous Random Walk Modified by Boundaries.- §4.6. Advantages of the Compensation Method. An Illustrative Example.- §4.7. Exploitation of the Structure of the Green Potential for the Homogeneous Random Walk.- §4.8. Similar Situations.- 5. Passage Time Densities in Birth-Death Processes; Distribution Structure.- §5.00. Introduction.- §5.1. Passage TimeDensities for Birth-Death Processes.- §5.2. Passage Time Moments for a Birth-Death Process.- §5.3. PF?, Complete Monotonicity, Log-Concavity and Log-Convexity.- §5.4. Complete Monotonicity and Log-Convexity.- §5.5. Complete Monotonicity in Time-Reversible Processes.- §5.6. Some Useful Inequalities for the Families CM and PF?.- §5.7. Log-Concavity and Strong Unimodality for Lattice Distributions.- §5.8. Preservation of Log-Concavity and Log-Convexity under Tail Summation and Integration.- §5.9. Relation of CM and PF? to IFR and DFR Classes in Reliability.- 6. Passage Times and Exit Times for More General Chains.- §6.00. Introduction.- §6.1. Passage Time Densities to a Set of States.- §6.2. Mean Passage Times to a Set via the Green Potential.- §6.3. Ruin Probabilities via the Green Potential.- §6.4. Ergodic Flow Rates in a Chain.- §6.5. Ergodic Exit Times, Ergodic Sojourn Times, and Quasi-Stationary Exit Times.- §6.6. The Quasi-Stationary Exit Time. A Limit Theorem.- §6.7. The Connection Between Exit Times and Sojourn Times. A Renewal Theorem.- §6.8. A Comparison of the Mean Ergodic Exit Time and Mean Ergodic Sojourn Time for Arbitrary Chains.- §6.9. Stochastic Ordering of Exit Times of Interest for Time-Reversible Chains.- §6.10. Superiority of the Exit Time as System Failure Time; Jitter.- 7. The Fundamental Matrix, and Allied Topics.- §7.00. Introduction.- §7.1. The Fundamental Matrix for Ergodic Chains.- §7.2. The Structure of the Fundamental Matrix for Time-Reversible Chains.- §7.3. Mean Failure Times and Ruin Probabilities for Systems with Independent Markov Components and More General Chains.- §7.4. Covariance and Spectral Density Structure for Time-Reversible Processes.- §7.5. A Central Limit Theorem.- §7.6. Regeneration Times andPassage Times-Their Relation For Arbitrary Chains.- §7.7. Passage to a Set with Two States.- 8. Rarity and Exponentiality.- §8.0. Introduction.- §8.1. Passage Time Density Structure for Finite Ergodic Chains; the Exponential Approximation.- §8.2. A Limit Theorem for Ergodic Regenerative Processes.- §8.3. Prototype Behavior: Birth-Death Processes; Strongly Stable Systems.- §8.4. Limiting Behavior of the Ergodic and Quasi-stationary Exit Time Densities and Sojourn Time Densities for Birth-Death Processes.- §8.5. Limit Behavior of Other Exit Times for More General Chains.- §8.6. Strongly Stable Chains, Jitter; Estimation of the Failure Time Needed for the Exponential Approximation.- §8.7. A Measure of Exponentiality in the Completely Monotone Class of Densities.- §8.8. An Error Bound for Departure from Exponentiality in the Completely Monotone Class.- §8.9. The Exponential Approximation for Time-Reversible Systems.- §8.10. A Relaxation Time of Interest.- 9. Stochastic Monotonicity.- §9.00. Introduction.- §9.1. Monotone Markov Matrices and Monotone Chains.- §9.2. Some Monotone Chains in Discrete Time.- §9.3. Monotone Chains in Continuous Time.- §9.4. Other Monotone Processes in Continuous Time.- References.