On It\^{o}'s formula for symmetric $\alpha $-stable L\'{e}vy process of index $1<\alpha\leq 2 $

Rachid Belfadli; Youssef Ouknine

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arXiv · 1003.5367

On It\^{o}'s formula for symmetric $\alpha $-stable L\'{e}vy process of index $1<\alpha\leq 2 $

Rachid Belfadli·Youssef Ouknine

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Abstract

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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Rachid Belfadli, Youssef Ouknine. 2010-03-28. On It\^{o}'s formula for symmetric $\alpha $-stable L\'{e}vy process of index $1<\alpha\leq 2 $. https://arxiv.org/abs/1003.5367

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