Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential

Abstract

Consider a Markovian standard semigroup P_t, t≥o, with potential kernel U=∫P_tdt on a locally compact space E. Let μ be a finite measure on E with locally finite potential μ^U and X_t, t≥O, the process having (P_t) as transition semigroup and μ as initial law. Then for a measure ν on E the following two statements are equivalent:

• (a) μ^U≥νU;

• (b) there exists a “randomized” stopping time T such that X_T is distributed according to ν.