Solvability of Kolmogorov-Fokker-Planck equations for vector jump processes and occupation time on hypersurfaces

Abstract

We study occupation time on hypersurface for Markov n-dimensional jump processes. Solvability and uniqueness of integro-differential Kolmogorov-Fokker-Planck with generalized functions in coefficients are investigated. Then these results are used to show that the occupation time on hypersurfaces does exist for the jump processes as a limit in variance for a wide class of piecewise smooth hypersurfaces, including some fractal type and moving surfaces. An analog of the Meyer-Tanaka formula is presented.