On Ordered Stopping Times of a Markov Process

Abstract

Let $X$ be a strong Markov process with potential kernel $U$. We show that if $(\nu_n)$ and $\mu$ are measures on the state space of $X$ such that $\nu_1 U \leq \nu_2 U \leq \cdots \leq \mu U$, then there is a decreasing sequence $(T_n)$ of randomized stopping times such that $\nu_n$ is the law of $X_{T_n}$ when the initial distribution of $X$ is $\mu$.