On Strassen's theorem on stochastic domination (Q1297724)

The present paper offers a complete and straightforward proof of Strassen's famous theorem about stochastic domination, see \textit{V. Strassen} [Ann. Math. Stat. 36, 423-439 (1965; Zbl 0135.18701)], and the attention is drawn to the original paper. The theorem states that if a distribution \(P\) on some space \((E,\leq)\) is dominated by another \(P'\), then there exists a joint distribution \(\widehat P\) on \(E^2\) with marginal distributions \(P\) and \(P'\) so that \(\widehat P(x\leq x')= 1\) holds. The proof is based on methods of functional analysis. It is well known that this result has various applications, for instance for Markov processes and for the coupling.