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

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

2010-03-28

arxiv.org/abs/1003.5367v2

Mathematics

Probability

This paper has been withdrawn by the author due to the incomplete presentation

Scientific paper

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 $\alpha$-stable L\'evy process, for $\alpha \in ]1,2]$, in one parameter case (resp, in two parameter case). We then apply these integrals to write the corresponding generalized It\^{o} formula. Furthermore, some approximations schemes of the area integral w.r.t local time are given.

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