Skorokhod Embedding by Randomized Hitting Times

Abstract

The “Skorokhod embedding” problem was solved for general strong Markov processes by Rost [R70,R71]: given such a process X = (X _t; t ≥ 0), an initial law μ with σ-finite potential, and a target law v, there is a randomized stopping time T such that

$${X_T} \sim v\quad when\quad {X_0} \sim \mu $$

(1.1)

if and only if the potential of μ dominates that of v. Subsequently various authors have shown that under additional hypotheses on X one can take T to be nonrandomized, i.e. a stopping time of the natural filtration of X. For recent work on this subject see [C85] and [FF90]; see also [Fa81,Fa83] which contain references for the earlier literature.

Research supported in part by NSF grant DMS 8721347.