The excursion measure away from zero for spectrally negative Levy processes

We provide a description of the excursion measure from a point for a spectrally negative Levy process. The description is based in two main ingredients. The first is building a spectrally negative Levy process conditioned to avoid zero and the study of its entrance law at zero. The latter is connected with both the excursion measure from zero of the process reflected in its infimum and reflected in its supremum. This leads us to establish a connection between the excursion measure from the state zero and the excursion measure from zero for the process reflected at the infimum and reflected at the supremum, respectively, which is the second main ingredient of our description.