Capacities on a finite lattice
Probability
2011-05-10 v1
Abstract
In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete monotonicity we can view a capacity as a marginal condition for probability distribution over the distributive lattice of dual order ideals. In this paper we discuss a combinatorial approach when capacities are defined over a finite lattice, and investigate Fr\'{e}chet bounds given the marginal condition, probabilistic interpretation of difference operators, and stochastic inequalities with completely monotone capacities.
Keywords
Cite
@article{arxiv.1105.1395,
title = {Capacities on a finite lattice},
author = {Motoya Machida},
journal= {arXiv preprint arXiv:1105.1395},
year = {2011}
}
Comments
20 pages