Stopped distributions for Markov processes in duality

Abstract

Let X and \(\hat X\) be standard Markov processes in duality on a state space E and assume that semipolar sets are polar. Let μ be a measure on E whose X measure-potential μ U is σ-finite. We characterize the measures v on E which arise as the Pμ-distribution of XTfor some non-randomized stopping time T. We then apply this result to characterize the measures v on E which satisfy v U ≦ μ U.