The theory of structured dependence has many real-life applications in areas such as finance, insurance, seismology, neuroscience, and genetics. The first book to be devoted to this research area, this is a useful tool for researchers and practitioners in the field, as well as graduate students.
The theory of structured dependence has many real-life applications in areas such as finance, insurance, seismology, neuroscience, and genetics. The first book to be devoted to this research area, this is a useful tool for researchers and practitioners in the field, as well as graduate students.
Tomasz R. Bielecki is Professor of Applied Mathematics at the Illinois Institute of Technology, Chicago. He co-authored Credit Risk: Modelling, Valuation and Hedging (2002), Credit Risk Modelling (2010) and Counterparty Risk and Funding (2014), and he currently serves as an associate editor of several journals, including Stochastics: An International Journal of Probability and Stochastic Processes.
Inhaltsangabe
1. Introduction Part I. Consistencies: 2. Strong Markov consistency of multivariate Markov families and processes 3. Consistency of finite multivariate Markov chains 4. Consistency of finite multivariate conditional Markov chains 5. Consistency of multivariate special semimartingales Part II. Structures: 6. Strong Markov family structures 7. Markov chain structures 8. Conditional Markov chain structures 9. Special semimartingale structures Part III. Further Developments: 10. Archimedean survival processes, Markov consistency, ASP structures 11. Generalized multivariate Hawkes processes Part IV. Applications of Stochastic Structures: 12. Applications of stochastic structures Appendix A. Stochastic analysis: selected concepts and results used in this book Appendix B. Markov processes and Markov families Appendix C. Finite Markov chains: auxiliary technical framework Appendix D. Crash course on conditional Markov chains and on doubly stochastic Markov chains Appendix E. Evolution systems and semigroups of linear operators Appendix F. Martingale problem: some new results needed in this book Appendix G. Function spaces and pseudo-differential operators References Notation index Subject index.
1. Introduction Part I. Consistencies: 2. Strong Markov consistency of multivariate Markov families and processes 3. Consistency of finite multivariate Markov chains 4. Consistency of finite multivariate conditional Markov chains 5. Consistency of multivariate special semimartingales Part II. Structures: 6. Strong Markov family structures 7. Markov chain structures 8. Conditional Markov chain structures 9. Special semimartingale structures Part III. Further Developments: 10. Archimedean survival processes, Markov consistency, ASP structures 11. Generalized multivariate Hawkes processes Part IV. Applications of Stochastic Structures: 12. Applications of stochastic structures Appendix A. Stochastic analysis: selected concepts and results used in this book Appendix B. Markov processes and Markov families Appendix C. Finite Markov chains: auxiliary technical framework Appendix D. Crash course on conditional Markov chains and on doubly stochastic Markov chains Appendix E. Evolution systems and semigroups of linear operators Appendix F. Martingale problem: some new results needed in this book Appendix G. Function spaces and pseudo-differential operators References Notation index Subject index.
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