Structured Dependence between Stochastic Processes

Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.

Tomasz R. Bielecki (Author), Jacek Jakubowski (Author), Mariusz Niew?g?owski (Author)

9781107154254, Cambridge University Press

Hardback, published 27 August 2020

278 pages
24 x 16.5 x 2.5 cm, 0.6 kg

The 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.

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.

Subject Areas: Volcanology & seismology [RBC], Neurosciences [PSAN], Genetics [non-medical PSAK], Stochastics [PBWL], Probability & statistics [PBT], Operational research [KJT], Insurance & actuarial studies [KFFN]