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Is there an extension of Ito's Lemma where $X_t$ is a semi-martingale and $f:\mathbb{R}^d \rightarrow \mathbb{R}$ is a function which is not smooth?

I've been looking but have not found much, any reference is appraciated.

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The non-smooth generalization of Ito's Lemma is called the Ito-Doeblin formula. Doeblin has a fascinating personal history.

https://en.wikipedia.org/wiki/Wolfgang_Doeblin

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    $\begingroup$ Every, instance of Ito-Dublin I know requires the f_x to exist... can you post a link to a version where $f_x$ is rough? $\endgroup$ – AIM_BLB Jan 12 '17 at 19:30
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There are versions available for convex $f$ and for $f\in H^1$. Some places to start are On semimartingale decompositions of convex functions of semimartingales (Carlen and Protter) and On Itô s formula for multidimensional Brownian motion (Follmer and Protter).

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