This is the first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory of mass transportation with emphasis on the Monge-Kantorovich mass transporation and the Kantorovich-Rubinstein mass transshipment problems, and their various extensions. They discuss a variety of different approaches toward solutions of these problems and exploit the rich interrelations to several mathematical sciences -- from fucntional analysis to probability theory and mathematical economics.
The second volume is devoted to applications of the mass transportation and mass transshipment problems to topics in applied probability, theory of moments and distributions with given marginals, queueing theory, risk theory, analysis of algorithms, and tomography. The authors provide an account of the theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations, stochastic algorithms, and rounding problems.
The books will be useful to graduate students and researchers in the fields of theoretical and applied probability, operations research, computer science, and mathematical economics. The prerequisites for this book are graduate-level probability theory and real and functional analysis.
Svetlozar T. Rachev is Professor of Statistics and Economics at the University of California, Santa Barbara. He has over 150 published papers as well as three monographs. His research areas include the theory of mass transportation problems, probability metrics, and mathematical finance. He is a Fellow of the Institute of Mathematical Statistics, Elected Member of the International Statistical Institute, and Foreign Member of the Russian Academy of Natural Sciences.
Ludger Rüschendorf is Chair-Professor in the Institute for Mathematical Stochastics at the University of Freiburg. He has published over 100 papers and a monograph on the theory of asymptotic statistics. His main research areas are the theory of mass transportation, probability metrics, stochastic algorithms, limit theorems for Gaussian and non-Gaussian laws, and mathematical statistics. He is a member of several mathematical and statistical societies and an Elected Member of the International Statistical Institute.