Barlow, M. T. Necessary and sufficient conditions for the continuity of local time of Lévy processes. (English) Zbl 0666.60072 Ann. Probab. 16, No. 4, 1389-1427 (1988). 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 Cited in 4 ReviewsCited in 29 Documents MSC: 60J55 Local time and additive functionals 60G17 Sample path properties 60J99 Markov processes Keywords:joint continuity of the local time process; Lévy processes; modulus of continuity Citations:Zbl 0584.60087 PDFBibTeX XMLCite \textit{M. T. Barlow}, Ann. Probab. 16, No. 4, 1389--1427 (1988; Zbl 0666.60072) Full Text: DOI