Drift transforms and Green function estimates for discontinuous processes

摘要

In this paper, we consider Girsanov transforms of pure jump type for discontinuous Markov processes. We show that, under some quite natural conditions, the Green functions of the Girsanov transformed process are comparable to those of the original process. As an application of the general results, the drift transform of symmetric stable processes is studied in detail. In particular, we show that the relativistic alpha-stable process in a bounded C-1,C-1-smooth open set D can be obtained from symmetric alpha-stable process in D through a combination of a pure jump Girsanov transform and a Feynman-Kac transform. From this, we deduce that the Green functions for these two processes in D are comparable. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 30]