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
The Institute of Mathematics and Mechanics, St. Petersburg State University, 198904, Russia
Received 31 January 2001; Revised 3 July 2001
Copyright © 2001 N. G. Dokuchaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.