An occupation time formula for semimartingales in ℝ^N

2013/12/11 by Andrea Bevilacqua, Bevilacqua, Andrea, Franco Flandoli +1
Mathematics · #60G30 #60G44 #60G57 #60Gxx #60H10 #60J55 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G30 #msc:60G44 #msc:60G57 #msc:60Gxx #msc:60H10 #msc:60J55

paper · pdf · doi:10.48550/arxiv.1312.3232

arxiv created 2013/12/11 · arxiv updated 2013/12/12

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.

Related

• A Generalized Occupation Time Formula For Continuous Semimartingales
• Geometric Deviation From Lévy's Occupation Time Arcsine Law
• Change of variable formula for local time of continuous semimartingale
• Occupation times and areas derived from random sampling
• Occupation times via Bessel functions