Structured Dependence Between Stochastic Processes

ISBN-13: 9781107154254 / Angielski / Twarda / 2020 / 278 str.

Tomasz R. Bielecki; Jacek Jakubowski; Mariusz Niewȩglowski

Opis

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.

Recenzje

'The authors follow good traditions, starting with exact definitions, commenting on essential properties, asking appropriate questions, formulating theorems, lemmas or propositions and giving explicit conditions under which complete proofs are provided for the statements.' Jordan M. Stoyanov, zbMATH

Spis treści

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.