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

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

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Bibliographic Details
Main Author: Barbu, Vlad Stefan
Other Authors: Vergne, Nicolas
Format: eBook
Language:English
Published: Newark : John Wiley & Sons, Incorporated, 2020.
Subjects:
Mathematical statistics.
Mathematical statistics
Online Access:Click for online access
Table of Contents:
  • 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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