The converse of a stochastic relation

Transition probabilities are proposed as the stochastic counterparts to set-based relations. We propose the construction of the converse of a stochastic relation. It is shown that two of the most useful properties carry over: the converse is idempotent as well as anticommutative. The nondeterminism inherent in a stochastic relation is defined and briefly investigated. We define a bisimulation relation, and indicate conditions under which this relation is transitive; moreover it is shown that bisimulation and converse are compatible.