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Authors: | Bevilacqua, Andrea* Flandoli, Franco* |
Title: | An occupation time formula for semimartingales in R^N | Journal: | Stochastic Processes and their Applications | Series/Report no.: | / 124 (2014) | Publisher: | Elsevier | Issue Date: | 2014 | DOI: | 10.1016/j.spa.2014.04.014 | Abstract: | Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in R^N 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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