An occupation time formula for semimartingales in R-N

作者：Bevilacqua A; Flandoli F^*

来源：Stochastic Processes and Their Applications, 2014, 124(10): 3342-3361.

DOI：10.1016/j.spa.2014.04.014

• Local time
• Coarea formula
• Occupation measure
• Manifolds

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.

• 出版日期2014-10