Structured Dependence between Stochastic Processes

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Tomasz R. Bielecki (Illinois Institute of Technology) Jacek Jakubowski (Uniwersytet Warszawski, Poland)

Structured Dependence between Stochastic Processes

Tomasz R. Bielecki (Illinois Institute of Technology), Jacek Jakubowski (Uniwersytet Warszawski, Poland), Mariusz Niewȩgłowski

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English

Cambridge University Press
27 August 2020

Insurance & actuarial studies; Operational research; Probability & statistics; Stochastics; Neurosciences

Series: Encyclopedia of Mathematics and its Applications

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.

By: Tomasz R. Bielecki (Illinois Institute of Technology), Jacek Jakubowski (Uniwersytet Warszawski, Poland), Mariusz Niewȩgłowski
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 165mm, Spine: 25mm
Weight: 600g
ISBN: 9781107154254
ISBN 10: 1107154251
Series: Encyclopedia of Mathematics and its Applications
Pages: 278
Publication Date: 27 August 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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. Jacek Jakubowski is Professor of Mathematics at the University of Warsaw. He is the author of numerous research papers in the areas of functional analysis, probability theory, stochastic processes, stochastic analysis, and mathematical finance, and he has co-authored several books in Polish, including Introduction to Probability Theory (2000), which is now in its fourth edition. Mariusz Niewȩgłowski is currently an Assistant Professor in the Faculty of Mathematics and Information Science at Warsaw University of Technology. The areas of his current research include financial mathematics with a focus on credit risk and stochastic analysis with a focus on modeling of dependence between stochastic processes.

Reviews for Structured Dependence between Stochastic Processes

'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