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2010 Local Time Rough Path for Lévy Processes
Chunrong Feng, Huaizhong Zhao
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Electron. J. Probab. 15: 452-483 (2010). DOI: 10.1214/EJP.v15-770


In this paper, we will prove that the local time of a Lévy process is a rough path of roughness $p$ a.s. for any $2 < p < 3$ under some condition for the Lévy measure. This is a new class of rough path processes. Then for any function $g$ of finite $q$-variation ($1\leq q <3$), we establish the integral $\int _{-\infty}^{\infty}g(x)dL_t^x$ as a Young integral when $1\leq q<2$ and a Lyons' rough path integral when $2\leq q<3$. We therefore apply these path integrals to extend the Tanaka-Meyer formula for a continuous function $f$ if $f^\prime_{-}$ exists and is of finite $q$-variation when $1\leq q<3$, for both continuous semi-martingales and a class of Lévy processes.


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Chunrong Feng. Huaizhong Zhao. "Local Time Rough Path for Lévy Processes." Electron. J. Probab. 15 452 - 483, 2010.


Accepted: 29 April 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1227.60071
MathSciNet: MR2639732
Digital Object Identifier: 10.1214/EJP.v15-770

Primary: 60H05
Secondary: 58J99


Vol.15 • 2010
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