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 ($1leq q <3$), we establish the integral $int _{-infty}^{infty}g(x)dL_t^x$ as a Young integral when $1leq q<2$ and a Lyons' rough path integral when $2leq q<3$. 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 $1leq q<3$, for both continuous semi-martingales and a class of Lévy processes.
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机译：在本文中，我们将证明Lévy过程的本地时间是粗糙度$ p $ a.s的粗略路径。在Lévy度量的某些条件下，任何$ 2 <3 $。这是一类新的粗糙路径过程。然后，对于任何具有有限$ q $变异（$ 1 leq q <3 $）的函数$ g $，我们建立积分$ int _ {- infty} ^ { infty} g（x）dL_t ^ x $当$ 1 leq q <2 $时为Young积分，而当$ 2 leq q <3 $时为里昂斯粗糙路径积分。因此，如果$ f ^ prime _ {-} $存在并且当$ 1 leq q <3 $时具有有限的$ q $变差，我们将应用这些路径积分来扩展Tanaka-Meyer公式，以获得连续函数$ f连续的半mart割和一类列维流程。
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