International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 11, Pages 637-652
doi:10.1155/S0161171201011760

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

N. G. Dokuchaev

 The Institute of Mathematics and Mechanics, St. Petersburg State University, 198904, Russia
Received 31 January 2001; Revised 3 July 2001

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.