Structured dependence between stochastic processes / Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski.

Format:

Book

Author/Creator:

Bielecki, Tomasz R., 1955- author.

Jakubowski, Jacek, author.

Niewęgłowski, Mariusz, 1976- author.

Series:

Encyclopedia of mathematics and its applications ; v. 175.

Encyclopedia of mathematics and its applications ; 175

Language:

English

Subjects (All):

Markov processes.

Dependence (Statistics).

Physical Description:

viii, 269 pages : illustrations ; 25 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.

Summary:

"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. Encyclopedia of Mathematics and Its Applications This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and Its Applications cover their subjects comprehensively. Less important results may be summarized as exercises at the ends of chapters. For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects"-- Provided by publisher.

Contents:

Strong Markov consistency of multivariate Markov families and processes

Consistency of finite multivariate Markov chains

Consistency of finite multivariate conditional Markov chains

Consistency of multivariate special semimartingales

Strong Markov family structures

Markov chain structures

Conditional Markov chain structures

Special semimartingale structures

Archimedean survival processes, Markov consistency, ASP structures

Generalized multivariate Hawkes processes

Applications of stochastic structures.

Notes:

Includes bibliographical references (pages 259-263) and indexes.

Other Format:

Online version: Bielecki, Tomasz R., 1955- Structured dependence between stochastic processes

ISBN:

9781107154254

1107154251

OCLC:

1155483264