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Stochastic monotonicity and realizable monotonicity. (English) Zbl 1015.60010
The authors explore and relate the notions of stochastic monotonicity and realizable monotonicity, for a system of probability measures on a common finite partially ordered set (poset) \(\mathcal{S}\) when the measures are indexed by another poset \(\mathcal{A}\). They give counterexamples to show that the two notions are not always equivalent. But for various large classes of \(\mathcal{S}\) they present conditions on the poset \(\mathcal{A}\) that are necessary and sufficient for equivalence.

MSC:
60E15 Inequalities; stochastic orderings
05C38 Paths and cycles
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