Mass Transportation Problems

Svetlozar T. Rachev is a Professor in Department of Applied Mathematics and Statistics, SUNY-Stony Brook.Ludger Rüschendorf, Professor of Mathematical Stochastics, studied Mathematics, Physics and Economics in Münster. Diploma thesis 1972 - PhD 1974 in Hamburg in Asymptotic Statistics - Habilitation thesis 1979 in Aachen in the area of stochastic ordering, masstransportation and Fréchet bounds - Professorships in Germany: 1981 - 1987 in Freiburg, 1987-1993 in Münster, 1993- in Freiburg. He is elected member of the ISI, and author and co-author of several books and about 180 research papers.

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 to the Monge-Kantorovich mass transportation and the Kantorovich- Rubinstein mass transshipment problems, and their various extensions. They discuss a variety of different approaches towards solutions of these problems and exploit the rich interrelations to several mathematical sciences--from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications to the mass transportation and mass transshipment problems to topics in applied probability, theory of moments and distributions with given marginals, queucing theory, risk theory of probability metrics and its applications to various fields, amoung them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations, stochastic algorithms and rounding problems. The book 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.

Mass transportation problems concern the optimal transfer of masses from one location to another. This first of two volumes will be the definitive reference for researchers in applied probability, operations research, computer science, and mathematical economics.

The Monge-Kantorovich Problem.- Explicit Results for the Monge-Kantorovich Problem.- Duality Theory for Mass Transfer Problems.- Applications of the Duality Theory.- Mass Transshipment Problems and Ideal Metrics.