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)
