Necessary and sufficient conditions for the continuity of local time of Lévy processes (Q1116548)

The author and \textit{J. Hawkes} [C. R. Acad. Sci., Paris, Sér. I 301, 237-239 (1985; Zbl 0584.60087)] obtained a sufficient condition for the joint continuity of the local time process \((x,t)\to L^ x_ t\), where \(L^ x_ t\) is local time at x, for a class of one-dimensional Lévy processes. In this paper, the author succeeds in showing that the sufficient condition is also necessary. In addition, he obtains an exact modulus of continuity for \(x\to L^ x_ t\) for a wide class of processes.