Drift transforms and Green function estimates for discontinuous processes |
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Authors: | Zhen-Qing Chen Renming Song |
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Affiliation: | a Department of Mathematics, University of Washington, Seattle, WA 98195, USA b Department of Mathematics, University of Illinois, Urbana, IL 61801, USA |
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Abstract: | 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 α-stable process in a bounded C1,1-smooth open set D can be obtained from symmetric α-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. |
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Keywords: | primary 60J45 60J40 secondary 35J10 47J20 |
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