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The Methods of Distances in the Theory of Probability and Statistics (Hardcover, 2013 ed.)
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The Methods of Distances in the Theory of Probability and Statistics (Hardcover, 2013 ed.)
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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)
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