On the Kantorovich–Rubinstein maximum principle for the Fortet–Mourier norm
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 107-121
MSC: Primary 60J25; Secondary 37J25.
DOI: 10.4064/ap86-2-2
Abstract
A new version of the maximum principle is presented. The classical Kantorovich–Rubinstein principle gives necessary conditions for the maxima of a linear functional acting on the space of Lipschitzian functions. The maximum value of this functional defines the Hutchinson metric on the space of probability measures. We show an analogous result for the Fortet–Mourier metric. This principle is then applied in the stability theory of Markov–Feller semigroups.
