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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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References:
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