The Converse of a Probabilistic Relation

Abstract

Transition probabilities are proposed as the stochastic counterparts to set-based relations. We propose the construction of the converse of a probabilistic relation. It is shown that two of the most useful properties carry over: the converse is idempotent, and anticommutative. The last property is shown to hold relative to some initial probability measure. This paper investigates the relation between stochastic and set-based relations through the support function of probabilities.