Multifractal structure of a general subordinator

The object of this paper is to obtain the multifractal structure for the local time of a general Lévy process which hits points. All such local time measures can be represented as the occupation measure of a subordinator. The thick points in the spectrum were investigated in a recent paper by Marsalle (1999. Ann. Probab. 27, 150–165). In this paper we obtain the spectrum for thin points, obtaining analogues of our results (Hu and Taylor, 1997, Stochastic Process. Appl. 66, 283–299) for the stable subordinator. We obtain our precise dimension results for exceptional sets in time rather than in space.