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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
  • Local Time
  • Coarea Formula
  • Occupation Measure
  • Manifolds
Disciplines
  • Mathematics

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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