# An occupation time formula for semimartingales in [formula omitted]

- Authors
- Journal
- Stochastic Processes and their Applications 0304-4149
- Publisher
- Elsevier
- Volume
- 124
- Issue
- 10
- Identifiers
- DOI: 10.1016/j.spa.2014.04.014
- Keywords
- Disciplines

## Abstract

Abstract Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in RN is proven. The occupation measure of a semimartingale, for N≥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.

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