On Strassen's Theorem on Stochastic Domination
Torgny Lindvall, Chalmers and GU
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.
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