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Principles of copula theory / Fabrizio Durante and Carlo Sempi.

By: Contributor(s): Material type: TextTextPublication details: Boca Raton : CRC Press, ©2016.Description: xvi, 315 p. : ill. ; 24 cmISBN:
  • 9781439884423 (hbk.)
Subject(s): DDC classification:
  • 000SA.07 23 D951
Contents:
1. Copulas : basic definitions and properties -- 2. Copulas and stochastic dependence -- 3. Copulas and measures -- 4. Copulas and approximation -- 5. The Markov product of copulas -- 6. A compendium of families of copulas -- 7. Generalisations of copulas : quasi-copulas -- 8. Generalisations of copulas : semi-copulas.
Summary: This book explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results. After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas, and discusses the Markov product for 2-copulas. The authors also examine selected families of copulas that possess appealing features from both theoretical and applied viewpoints. The book concludes with in-depth discussions on two generalizations of copulas: quasi- and semi-copulas. Although copulas are not the solution to all stochastic problems, they are an indispensable tool for understanding several problems about stochastic dependence. This book gives you the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures.
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Includes bibliographical references and index.

1. Copulas : basic definitions and properties --
2. Copulas and stochastic dependence --
3. Copulas and measures --
4. Copulas and approximation --
5. The Markov product of copulas --
6. A compendium of families of copulas --
7. Generalisations of copulas : quasi-copulas --
8. Generalisations of copulas : semi-copulas.

This book explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results. After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas, and discusses the Markov product for 2-copulas. The authors also examine selected families of copulas that possess appealing features from both theoretical and applied viewpoints. The book concludes with in-depth discussions on two generalizations of copulas: quasi- and semi-copulas. Although copulas are not the solution to all stochastic problems, they are an indispensable tool for understanding several problems about stochastic dependence. This book gives you the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures.

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