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International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 11, Pages 637-652
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.