@article{ECP1005,
author = {Torgny Lindvall},
title = {On Strassen's Theorem on Stochastic Domination},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {4},
year = {1999},
keywords = {Strassen's theorem, coupling, pre-ordering, maximal diagonal probability},
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.},
pages = {no. 7, 51-59},
issn = {1083-589X},
doi = {10.1214/ECP.v4-1005},
url = {http://ecp.ejpecp.org/article/view/1005}}