Statistical Topics and Stochastic Models for Dependent Data with Applications

1. Auflage 2020
ISBN: 978-1-78630-603-6
Verlag: Wiley

Buch, Englisch, 288 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 589 g

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.

Autoren/Hrsg.

Barbu, Vlad Stefan

Vergne, Nicolas

Fachgebiete

• Sozialwissenschaften Pädagogik Lehrerausbildung, Unterricht & Didaktik Allgemeine Didaktik Naturwissenschaften, Mathematik (Unterricht & Didaktik)
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Sozialwissenschaften Pädagogik Pädagogik Bildungssystem Curricula: Planung und Entwicklung

Inhaltsverzeichnis

Preface xi
Vlad Stefan BARBU and Nicolas VERGNE

Part 1. Markov and Semi-Markov Processes 1

Chapter 1. Variable Length Markov Chains, Persistent Random Walks: A Close Encounter 3
Peggy CÉNAC, Brigitte CHAUVIN, Frédéric PACCAUT and Nicolas POUYANNE

1.1. Introduction 3

1.2. VLMCs: definition of the model 6

1.3. Definition and behavior of PRWs 9

1.3.1. PRWs in dimension one 9

1.3.2. PRWs in dimension two 13

1.4. VLMC: existence of stationary probability measures 15

1.5. Where VLMC and PRW meet 19

1.5.1. Semi-Markov chains and Markov additive processes 19

1.5.2. PRWs induce semi-Markov chains 20

1.5.3. Semi-Markov chain of the a-LIS in a stable VLMC 22

1.5.4. The meeting point 23

1.6. References 27

Chapter 2. Bootstraps of Martingale-difference Arrays Under the Uniformly Integrable Entropy 29
Salim BOUZEBDA and Nikolaos LIMNIOS

2.1. Introduction and motivation 29

2.2. Some preliminaries and notation 30

2.3. Main results 35

2.4. Application for the semi-Markov kernel estimators 36

2.5. Proofs 41

2.6. References 45

Chapter 3. A Review of the Dividend Discount Model: From Deterministic to Stochastic Models 47
Guglielmo D’AMICO and Riccardo DE BLASIS

3.1. Introduction 47

3.2. General model 48

3.3. Gordon growth model and extensions 50

3.3.1. Gordon model 50

3.3.2. Two-stage model 51

3.3.3. H model 52

3.3.4. Three-stage model 52

3.3.5. N-stage model 53

3.3.6. Other extensions 53

3.4. Markov chain stock models 54

3.4.1. Hurley and Johnson model 54

3.4.2. Yao model 56

3.4.3. Markov stock model 57

3.4.4. Multivariate Markov chain stock model 61

3.5. Conclusion 64

3.6. References 65

Chapter 4. Estimation of Piecewise-deterministic Trajectories in a Quantum Optics Sc

Über Autor(innen)

Vlad Stefan Barbu is Associate Professor in Statistics with LMRS at the University of Rouen Normandy, France. His main research focuses on statistics of stochastic processes and on techniques based on divergence measures, with a particular interest in semi-Markov and hidden semi-Markov processes.

Nicolas Vergne is Associate Professor in Statistics with LMRS at the University of Rouen Normandy. His research work is in statistics, focusing on different Markov-type models: drifting Markov models, semi-Markov models, hidden Markov models and bioinformatics.