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Table of contents (26 chapters)
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Front Matter
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General topics in the theory of probability metrics
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Front Matter
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Relations between compound, simple and primary distances
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Front Matter
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Applications of minimal probability distances
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Front Matter
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Ideal metrics
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Front Matter
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About this book
This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics.
After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.
Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)
Reviews
From the book reviews:
“This textbook gives a comprehensive overview of the method of metric distances and its applications in probability theory. … The text is mainly self-contained and should be accessible for readers with basic knowledge in probability theory. The exposition is well structured and covers an impressive range of topics around the central theme of probability metrics.” (Hilmar Mai, zbMATH, Vol. 1280, 2014)
“The reviewed book is divided into five parts. … The target audience is graduate students in the areas of functional analysis, geometry, mathematical programming, probability, statistics, stochastic analytics, and measure theory. The book can also be used for students in probability and statistics. The theory of probability metrics presented here can be applied to engineering, physics, chemistry, information theory, economics, and finance. Specialists from the aforementioned areas might find the book useful.” (Adriana Horníková, Technometrics, Vol. 55 (4), November, 2013)
Authors and Affiliations
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Inst. Statistik und Mathematische, Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe, Germany
Svetlozar T. Rachev
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, Department of Probability and Statistics, Charles University, Prague, Czech Republic
Lev B. Klebanov
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, EDHEC-Risk Institute, EDHEC Business School, Singapore, Singapore
Stoyan V. Stoyanov
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New Hope, USA
Frank Fabozzi
About the authors
Bibliographic Information
Book Title: The Methods of Distances in the Theory of Probability and Statistics
Authors: Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank Fabozzi
DOI: https://doi.org/10.1007/978-1-4614-4869-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2013
Hardcover ISBN: 978-1-4614-4868-6Published: 03 January 2013
Softcover ISBN: 978-1-4899-9569-8Published: 26 June 2015
eBook ISBN: 978-1-4614-4869-3Published: 04 January 2013
Edition Number: 1
Number of Pages: XVI, 619
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Approximations and Expansions