@article{EJP770,
author = {Chunrong Feng and Huaizhong Zhao},
title = {Local Time Rough Path for Lévy Processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {semimartingale local time; geometric rough path; Young integral; rough path integral; L'evy processes},
abstract = {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.},
pages = {no. 16, 452-483},
issn = {1083-6489},
doi = {10.1214/EJP.v15-770},
url = {http://ejp.ejpecp.org/article/view/770}}