Mass Transportation Problems: Volume 1: Theory

ISBN-13: 9781475785258 / Angielski / Miękka / 2013 / 508 str.

Svetlozar T. Rachev;Ludger Ruschendorf

Opis

1.1 Mass Transportation Problems in Probability Theory This chapter provides a basic introduction to mass transportation pr- lems (MTPs). We introduce some of the methods used in studying MTPs: dualrepresentations, explicitsolutions, topologicalproperties.Weshallalso discuss some applications of MTPs. The following measure-theoretic problems are well-known continuous casesofMKPs(see, forexample, Dudley(1976), LevinandMilyutin(1979), R] uschendorf (1979, 1981), Kemperman (1983), Kellerer (1984), Rachev (1984b, 1991c) and the references therein). TheMonge Kantorovichmasstransportationproblem(MKP): Given?xed probability measuresP andP on a separable metric spaceS and a mea- 1 2 surable cost functionc on the Cartesian productSxS, ?nd u (P, P ) = inf c(x, y)P(dx, dy), (1.1.1) c 1 2 wherethein?mumistakenoverallprobabilitymeasuresP onSxS having projections ?P = P, i=1,2. (1.1.2) i i 2 1. Introduction The Kantorovich Rubinstein transshipment problem (KRP): GivenP 1 andP onS ?nd 2 ? u (P, P ) = inf c(x, y)Q(dx, dy), (1.1.3) 1 2 c where the in?mum is taken over all ?nite measuresQ onSxS having the marginal di?erence ?Q Q = P ?P; (1.1.4) 1 2 1 2 that is, Q(AxS)?Q(SxA)=P (A)?P (A) for all Borel setsA?S."

Spis treści

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.

O autorze

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.