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On Strassen's Theorem on Stochastic Domination


 
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1. Title Title of document On Strassen's Theorem on Stochastic Domination
 
2. Creator Author's name, affiliation, country Torgny Lindvall; Chalmers and GU
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Strassen's theorem, coupling, pre-ordering, maximal diagonal probability
 
3. Subject Subject classification 60B05, 60E15, 60J10
 
4. Description Abstract The purpose of this note is to make available a reasonably complete and straightforward proof of Strassen's theorem on stochastic domination, and to draw attention to the original paper. We also point out that the maximal possible value of $P(Z = Z')$ is actually not reduced by the requirement $Z \leq Z'$. Here, $Z,Z'$ are stochastic elements that Strassen's theorem states exist under a stochastic domination condition. The consequence of that observation to stochastically monotone Markov chains is pointed out. Usually the theorem is formulated with the assumption that $\leq$ is a partial ordering; the proof reveals that a pre-ordering suffices.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-06-01
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1005
 
10. Identifier Digital Object Identifier 10.1214/ECP.v4-1005
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 4
 
12. Language English=en
 
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