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Markov Chain Models - Rarity and Exponentiality - J. Keilson
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Markov Chain Models - Rarity and Exponentiality - edizione con copertina flessibile

ISBN: 9780387904054

Paperback, [PU: Springer-Verlag New York Inc.], in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the mate… Altro …

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Keilson, J.:

Markov Chain Models ¿ Rarity and Exponentiality - edizione con copertina flessibile

1979, ISBN: 0387904050

Softcover reprint of the original 1st ed. 1979 Kartoniert / Broschiert Wahrscheinlichkeitsrechnung und Statistik, Markovchain; MarkowscheKette; Variance; Uniformization; regenerativepro… Altro …

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J. Keilson:
Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences) - edizione con copertina flessibile

1979

ISBN: 0387904050

[EAN: 9780387904054], [SC: 0.0], [PU: Springer], Befriedigend/Good: Durchschnittlich erhaltenes Buch bzw. Schutzumschlag mit Gebrauchsspuren, aber vollständigen Seiten. / Describes the av… Altro …

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Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences, Band 28). - edizione con copertina flessibile

1979, ISBN: 0387904050

[EAN: 9780387904054], [PU: New York Inc.: Springer-Verlag], Applied Mathematical Sciences, Band 28. Zust: Gutes Exemplar. XIII, 184 Seiten, Englisch 348g, Books

Costi di spedizione: EUR 3.00 Antiquariat Bernhardt, Kassel, Germany [627145] [Rating: 5 (von 5)]
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Keilson, Julian:
Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences, Band 28) - libri usati

1979, ISBN: 9780387904054

XIII, 184 Seiten, Broschiert Applied Mathematical Sciences, Band 28. Zust: Gutes Exemplar. Versand D: 3,00 EUR , [PU:New York Inc.: Springer-Verlag]

Costi di spedizione:Versandkosten innerhalb der BRD. (EUR 3.00) Antiquariat Bernhardt, 34121 Kassel

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Markov Chain Models - Rarity and Exponentiality

in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over­ view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat­ erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class

Informazioni dettagliate del libro - Markov Chain Models - Rarity and Exponentiality


EAN (ISBN-13): 9780387904054
ISBN (ISBN-10): 0387904050
Copertina rigida
Copertina flessibile
Anno di pubblicazione: 1979
Editore: SPRINGER VERLAG GMBH
208 Pagine
Peso: 0,318 kg
Lingua: eng/Englisch

Libro nella banca dati dal 2008-02-29T08:19:39+01:00 (Zurich)
Pagina di dettaglio ultima modifica in 2023-07-27T07:53:36+02:00 (Zurich)
ISBN/EAN: 0387904050

ISBN - Stili di scrittura alternativi:
0-387-90405-0, 978-0-387-90405-4
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : keilson
Titolo del libro: chain, markov chains, graduate text mathematics


Dati dell'editore

Autore: J. Keilson
Titolo: Applied Mathematical Sciences; Markov Chain Models — Rarity and Exponentiality
Editore: Springer; Springer US
184 Pagine
Anno di pubblicazione: 1979-04-23
New York; NY; US
Lingua: Inglese
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.

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