Open Access
Translator Disclaimer
April 2001 Stochastic Monotonicity and Realizable Monotonicity
James Allen Fill, Motoya Machida
Ann. Probab. 29(2): 938-978 (April 2001). DOI: 10.1214/aop/1008956698


We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) $\mathscr{S}$ when the measures are indexed by another poset $\mathscr{A}$. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of $\mathscr{S}$ we also present conditions on the poset $\mathscr{A}$ that are necessary and sufficient for equivalence. When $\mathscr{A} = \mathscr{S}$ , the condition that the cover graph of $\mathscr{S}$ have no cycles is necessary and sufficient for equivalence. This case arises in comparing applicability of the perfect sampling algorithms of Propp and Wilson and the first author of the present paper.


Download Citation

James Allen Fill. Motoya Machida. "Stochastic Monotonicity and Realizable Monotonicity." Ann. Probab. 29 (2) 938 - 978, April 2001.


Published: April 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1015.60010
MathSciNet: MR1849183
Digital Object Identifier: 10.1214/aop/1008956698

Primary: 60E05
Secondary: 05C38 , 06A06 , 60J10

Keywords: cycle , inverse probability transform , marginal problem , monotonicity equivalence , ‎partially ordered set , perfect sampling , Realizable monotonicity , rooted tree , Stochastic monotonicity , Strassen's theorem

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 2 • April 2001
Back to Top