New results on Hunt's hypothesis (H) for L\'evy processes
Abstract
In this paper, we present new results on Hunt's hypothesis (H) for L\'evy processes. We start with a comparison result on L\'evy 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\'evy processes satisfying (H). Finally, we construct a type of subordinators that does not satisfy Rao's condition.
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