On the potential theory of raw time changes (Q2752134)

The main goal of this paper is two exhibit new examples of Lévy processes satisfying Hunt's hypothesis but not the usual criterions (symmetry, Kanda's assumption on the Lévy-Khinchin exponent, stable subordination) ensuring it. Those Lévy processes are valued on the grid \({\mathbb Z}^d\) and have absolutely continuous resolvent, so that Hunt's hypothesis is equivalent to the bounded maximum principle as well as the bounded energy principle. The main result of the paper under review states that the latter principle is verified when the Lévy process is obtained through a certain raw time-change (right-inverse of a certain continuous non adapted additive functional involving the first jump valued on a fixed compact set of \({\mathbb Z} ^d)\) of another symmetric Lévy process on \({\mathbb Z}^d.\)NEWLINENEWLINEFor the entire collection see [Zbl 0964.00043].