Statistical Topics and Stochastic Models for Dependent Data with Applications Applications in Reliability, Survival Analysis and Related Fields.

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Barbu, Vlad Stefan
Otros Autores: Vergne, Nicolas
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2020.
Temas:
Mathematical statistics.
Mathematical statistics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Part 1 Markov and Semi-Markov Processes
  • Chapter 1 Variable Length Markov Chains, Persistent Random Walks: A Close Encounter
  • 1.1. Introduction
  • 1.2. VLMCs: definition of the model
  • 1.3. Definition and behavior of PRWs
  • 1.3.1. PRWs in dimension one
  • 1.3.2. PRWs in dimension two
  • 1.4. VLMC: existence of stationary probability measures
  • 1.5. Where VLMC and PRW meet
  • 1.5.1. Semi-Markov chains and Markov additive processes
  • 1.5.2. PRWs induce semi-Markov chains
  • 3.3.2. Two-stage model
  • 3.3.3. H model
  • 3.3.4. Three-stage model
  • 3.3.5. N-stage model
  • 3.3.6. Other extensions
  • 3.4. Markov chain stock models
  • 3.4.1. Hurley and Johnson model
  • 3.4.2. Yao model
  • 3.4.3. Markov stock model
  • 3.4.4. Multivariate Markov chain stock model
  • 3.5. Conclusion
  • 3.6. References
  • Chapter 4 Estimation of Piecewise-deterministic Trajectories in a Quantum Optics Scenario
  • 4.1. Introduction
  • 4.1.1. The postulates of quantum mechanics
  • 4.1.2. Dynamics of open quantum Markovian systems
  • 4.1.3. Stochastic wave function: quantum dynamics as PDPs
  • 4.1.4. Estimation for PDPs
  • 4.2. Problem formulation
  • 4.2.1. Atom-field interaction
  • 4.2.2. Piecewise-deterministic trajectories
  • 4.2.3. Measures
  • 4.3. Estimation procedure
  • 4.3.1. Strategy
  • 4.3.2. Least-square estimators
  • 4.3.3. Numerical experiments
  • 4.4. Physical interpretation
  • 4.5. Concluding remarks
  • 4.6. References
  • Chapter 5 Identification of Patterns in a Semi-Markov Chain
  • 5.1. Introduction
  • 5.2. The prefix chain
  • 5.3. The semi-Markov setting
  • 5.4. The hitting time of the pattern
  • 5.5. A genomic application
  • 5.6. Concluding remarks
  • 5.7. References
  • Part 2 Autoregressive Processes
  • Chapter 6 Time Changes and Stationarity Issues for Continuous Time Autoregressive Processes of Order
  • 6.1. Introduction
  • 6.2. Basics
  • 6.3. Stationary AR processes
  • 6.3.1. Formulas for the two first-order moments
  • 6.3.2. Examples
  • 6.3.3. Conditions for stationarity of CAR1(p) processes
  • 6.4. Time transforms
  • 6.4.1. Properties of time transforms
  • 6.4.2. MS processes
  • 6.5. Conclusion
  • 6.6. Appendix
  • 6.7. References
  • Chapter 7 Sequential Estimation for Non-parametric Autoregressive Models
  • 7.1. Introduction
  • 7.2. Main conditions

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