In this paper, we present new results on Hunt's hypothesis (H) for L\'{ e}vy processes. We start with a comparison result on L\'{ e}vy processes which implies that big jumps have no effect on the validity of (H). Based on this result and the Kanda-Forst-Rao theorem, we give examples of subordinators satisfying (H). Afterwards we give a new necessary and sufficient condition for (H) and obtain an extended Kanda-Forst-Rao theorem. By virtue of this theorem, we give a new class of L\'{ e}vy processes satisfying (H). Finally, we construct a type of subordinators that does not satisfy Rao's condition.
Categories: math.PR