Multistate Models in Earthquake Modeling

Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi- )Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7. This book is mainly intended for statisticians, mathematicians working in applied probability, and theoretically-oriented geophysicists and engineers interested in semi-Markov process theories, but it could be equally supportive to Master's and PhD students and professional researchers interested in stochastic modeling for probing the nature of earthquake phenomena.;Fundamentals on stress changes -- Hidden Markov models -- HIdden Markov renewal models -- Hitting time intensity -- Models comparison. Content: Cover Half-Title Page Dedication Title Page Copyright Page Contents List of Abbreviations List of Symbols Preface Introduction I.1. Motivation and objectives I.2. Seismic hazard assessment I.3. Earthquake occurrence models I.3.1. Stress release models I.3.2. Stress-based models I.3.3. Renewal models I.3.4. Markov and semi-Markov models I.3.5. Hidden (semi- )Markov models 1. Fundamentals on Stress Changes 1.1. Introduction 1.2. Stress interaction 1.3. Stress changes calculation 1.4. Modeling of Coulomb stress changes for different faulting types 2.4.4. Steps number for the first earthquake occurrence2.5. Conclusion 3. Hidden Markov Renewal Models 3.1. Introduction 3.2. Semi-Markov framework 3.3. Hidden Markov renewal framework 3.4. Modeling earthquakes in Greece 3.4.1. Hitting times and earthquake occurrence numbers 3.5. Conclusion 4. Hitting Time Intensity 4.1. Introduction 4.2. DTIHT for semi-Markov chains 4.2.1. Statistical estimation of the DTIHT 4.3. DTIHT for hidden Markov renewal chains 4.4. Conclusion 5. Models Comparison 5.1. Introduction 5.2. Markov framework 5.2.1. HMM case 5.2.2. HMRM case 5.3. Markov renewal framework5.3.1. HMM case 5.3.2. HMRM case 5.4. Conclusion Discussion & Concluding Remarks Appendices Appendix 1: Markov Models Appendix 2: Hidden Markov Models A2.1. Scoring or evaluation problem A2.1.1. Estimation or training problem A2.1.2. Decoding or alignment problem Appendix 3: Dataset References Index Other titles from iSTE in Mathematics and Statistics EULA