On Itô's formula for symmetric $α$-stable Lévy process of index $1<α\leq 2$

We use Young integration (resp, bounded $p,q$-variation theory introduced in \cite{Feng-Zhao}) to establish integration of determinate functions with respect to local time of symmetric $α$-stable Lévy process, for $α\in ]1,2]$, in one parameter case (resp, in two parameter case). We then apply these integrals to write the corresponding generalized Itô formula. Furthermore, some approximations schemes of the area integral w.r.t local time are given.

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