Capacities on a finite lattice

Details Capacities on a finite lattice Capacities on a finite lattice

2011-05-06

arxiv.org/abs/1105.1395v1

Mathematics

Probability

20 pages

Scientific paper

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.

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