# zbMATH — the first resource for mathematics

Necessary and sufficient conditions for the continuity of local time of Lévy processes. (English) Zbl 0666.60072
The author and 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.
Reviewer: J.B.Mitro

##### MSC:
 60J55 Local time and additive functionals 60G17 Sample path properties 60J99 Markov processes
Full Text: