Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in RNRN is proven. The occupation measure of a semimartingale, for N≥2N≥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.

An occupation time formula for semimartingales in RN

FLANDOLI, FRANCO
2014

Abstract

Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in RNRN is proven. The occupation measure of a semimartingale, for N≥2N≥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.
A., Bevilacqua; Flandoli, Franco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/761965
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