The Methods of Distances in the Theory of Probability and Statistics

Authors: Rachev, S.T., Klebanov, L., Stoyanov, S.V., Fabozzi, F.

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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)

About the authors

Svetlozar T. Rachev is a Professorin Department of Applied Mathematics and Statistics, SUNY-Stony Brook. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, MFF, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor of Finance, EDHEC Business School, Head of Research, EDHEC-Risk Institute. Frank J. Fabozzi is a Professor of Finance, EDHEC Business School

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)


Table of contents (26 chapters)

  • Main Directions in the Theory of Probability Metrics

    Rachev, Svetlozar T. (et al.)

    Pages 1-7

  • Probability Distances and Probability Metrics: Definitions

    Rachev, Svetlozar T. (et al.)

    Pages 11-31

  • Primary, Simple, and Compound Probability Distances and Minimal and Maximal Distances and Norms

    Rachev, Svetlozar T. (et al.)

    Pages 33-66

  • A Structural Classification of Probability Distances

    Rachev, Svetlozar T. (et al.)

    Pages 67-105

  • Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms

    Rachev, Svetlozar T. (et al.)

    Pages 109-143

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-1-4614-4869-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-1-4614-4868-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4899-9569-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Methods of Distances in the Theory of Probability and Statistics
Authors
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-4869-3
DOI
10.1007/978-1-4614-4869-3
Hardcover ISBN
978-1-4614-4868-6
Softcover ISBN
978-1-4899-9569-8
Edition Number
1
Number of Pages
XVI, 619
Topics