Density in small time for Lévy processes

The density of real-valued L evy processes is studied in small time under the assumption that the process has many small jumps.We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a nite number of jumps (-accessible points) the set of points that the process can reach with an innite number of jumps (asymptotically -accessible points) and the set of points that the process cannot reach b y jumping (-inaccessible points).