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Statistical topics and stochastic models for dependent data with applications : applications in reliability, survival analysis and related fields

Barbu, Vlad Stefan.

Statistical topics and stochastic models for dependent data with applications : applications in reliability, survival analysis and related fields

Barbu, Vlad Stefan.

9781119779421

9781119779414

London : ISTE, Ltd. ; Hoboken : Wiley, 2020.

1 online resource (281 pages)

Mathematics and statistics

Mathematics and statistics series (ISTE)

7.3. Pointwise estimation with absolute error risk.

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

This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.

John Wiley and Sons

Mathematical statistics.

Stochastic processes.

Stochastic Processes

Processus stochastiques.

Mathematical statistics

Barbu, Vlad Stefan.

Vergne, Nicolas.

https://onlinelibrary.wiley.com/doi/book/10.1002/9781119779421