Two Theorems on Hunt's Hypothesis (H) for Markov Processes

Ze-Chun Hu, Wei Sun, Li-Fei Wang

Published 2019-02-28Version 1

We investigate the invariance of Hunt's hypothesis (H) for Markov processes under two classes of transformations, which are change of measure and subordination. Our first theorem shows that for two standard processes $(X_t)$ and $(Y_t)$, if $(X_t)$ satisfies (H) and $(Y_t)$ is locally absolutely continuous with respect to $(X_t)$, then $(Y_t)$ satisfies (H). Our second theorem shows that a standard process $(X_t)$ satisfies (H) if and only if $(X_{\tau_t})$ satisfies (H) for some (and hence any) subordinator $(\tau_t)$ which is independent of $(X_t)$ and has a positive drift coefficient. Applications of the two theorems are given.