Structured Dependence between Stochastic Processes
Structured Dependence between Stochastic Processes
Jacek Jakubowski, Uniwersytet Warszawski, Poland
Mariusz Niewȩgłowski, Politechnika Warszawska, Poland
£110.00
GBPThe relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.
- Provides a consistent presentation of mathematical methods used for the purpose of analysis and modeling of structured dependence between random processes
- Summarizes the underlying non-standard required mathematical material to make the theory accessible to readers without specialized training
- Includes numerous examples of existing and potential applications of the theory as well as theoretical examples, making it a suitable reference for practitioners in these fields
Reviews & endorsements
'This is a timely book on an important topic, and it is well written.' John Masson Noble, MathSciNet
'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
Product details
August 2020Hardback
9781107154254
278 pages
240 × 165 × 25 mm
0.6kg
Available
Table of Contents
- 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.
