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October, 1988 Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes
M. T. Barlow
Ann. Probab. 16(4): 1389-1427 (October, 1988). DOI: 10.1214/aop/1176991576

Abstract

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.

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M. T. Barlow. "Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes." Ann. Probab. 16 (4) 1389 - 1427, October, 1988. https://doi.org/10.1214/aop/1176991576

Information

Published: October, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0666.60072
MathSciNet: MR958195
Digital Object Identifier: 10.1214/aop/1176991576

Subjects:
Primary: 60J55
Secondary: 60G17 , 60J30

Keywords: Levy process , Local time , Markov process

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 4 • October, 1988
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