A large class of Markov processes satisfying Hunt's hypothesis (H) is displayed. In particular, if $\Phi$ is a Levy-Khinchin exponent, then the Levy process with exponent $\Phi^\alpha (0 < \alpha < 1)$ satisfies (H). That is, every semipolar set is polar.
"Hunt's Hypothesis (H) and Getoor's Conjecture." Ann. Probab. 14 (3) 1085 - 1087, July, 1986. https://doi.org/10.1214/aop/1176992463