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Structured Dependence between Stochastic Processes

$125.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2020
  • availability: Available
  • format: Hardback
  • isbn: 9781107154254

$ 125.00 (C)

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About the Authors
  • 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.

    • 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
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    Product details

    • Date Published: August 2020
    • format: Hardback
    • isbn: 9781107154254
    • length: 278 pages
    • dimensions: 240 x 165 x 25 mm
    • weight: 0.6kg
    • availability: 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
    Notation index
    Subject index.

  • Authors

    Tomasz R. Bielecki, Illinois Institute of Technology
    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, Uniwersytet Warszawski, Poland
    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, Politechnika Warszawska, Poland
    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.

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