Kusuoka-Stroock formula on configuration space and regularities of local times with jumps
The purpose of this article is to establish some smoothness and quasi-sure existence results, for local times of discontinuous semimartingales, in the framework of Wiener-Poisson space of configurations. To this end, a Kusuoka-Strook commutation formula, between gradient and stochastic integration, is needed. Since there is no parallel transport on the configuration space, to mimic the classical continuous case of Wiener space is not straightforward, and some adaptation is necessary. Thus, the authors begin with the notion of a measurable field of Hilbert spaces over the probability space, and construct a version of Itô calculus, for integrands which take their values in a Hilbert space which changes with the path. Then, they establish a Kusuoka-Stroock formula in this setting, and deduce fractional Sobolev regularities and quasi-sure existence, for local times with jumps.
scientific article; zbMATH DE number 5162164
scientific article