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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

60J55 Local time and additive functionals
60G17 Sample path properties
60J99 Markov processes
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