An occupation time formula for semimartingales in ${\mathbb{R}}^N$

Abstract

Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in ${\mathbb{R}}^N$ is proven. The occupation measure of a semimartingale, for $N\ge 2$, is singular with respect to Lebesgue measure but it has a bounded density "transversal" to a foliation, under proper assumptions. In the particular case of the foliation given locally by the distance function from a manifold, the transversal density is related to a geometric local time of the semimartingale at the manifolds of the foliation.

References in corpus (1)

• On the characterization of some classes of proximally smooth sets