The Annals of Probability

Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes

M. T. Barlow

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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.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1389-1427.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991576

Digital Object Identifier
doi:10.1214/aop/1176991576

Mathematical Reviews number (MathSciNet)
MR958195

Zentralblatt MATH identifier
0666.60072

JSTOR
links.jstor.org

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 60G17: Sample path properties 60J30

Keywords
Markov process Levy process local time

Citation

Barlow, M. T. Necessary and Sufficient Conditions for the Continuity of Local Time of Levy Processes. Ann. Probab. 16 (1988), no. 4, 1389--1427. doi:10.1214/aop/1176991576. https://projecteuclid.org/euclid.aop/1176991576


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