Continuity of symmetric stable processes (original) (raw)

The path continuity of a symmetric p-stable process is examined in terms of any stochastic integral representation for the process. When 0 < p < 1, we give necessary and suflicient conditions for path continuity in terms of any (every) representation. When 1 &p<2, we extend the known sutliciency condition in terms of metric entropy and offer a conjecture for the stable version of the Dudley-Fernique theorem. Finally, necessary and sufficient conditions for path continuity are given in terms of continuity at a point for 0 < p < 2.