Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes
Barlow, M. T.
Ann. Probab., Tome 16 (1988) no. 4, p. 1389-1427 / Harvested from Project Euclid
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Let $u_1(x)$ be the 1-potential kernel density for a Levy process, let $\phi^2(x) = 2u_1(0) - u_1(x) - u_1(-x)$, let $\bar{\phi}$ be the monotone rearrangement of $\phi$ and let $I(\bar{\phi}) = \int_{0+} \phi(u)u^{-1}(\log(1/u))^{-1/2} du$. Barlow and Hawkes proved that if $I(\bar{\phi}) < \infty$, then the local time has a jointly continuous version. In this paper it is shown that if $I(\bar{\phi}) < \infty$, then the local time is not continuous.
Publié le : 1988-10-14
Classification:  Markov process,  Levy process,  local time,  60J55,  60G17,  60J30 
@article{1176991576,
     author = {Barlow, M. T.},
     title = {Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 1389-1427},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991576}
}

Barlow, M. T. Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes. Ann. Probab., Tome 16 (1988) no. 4, pp.  1389-1427. http://gdmltest.u-ga.fr/item/1176991576/