Drift transforms and Green function estimates for discontinuous processes

Zhen Qing Chen, Renming Song

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)262-281
Number of pages20
JournalJournal of Functional Analysis
Issue number1
StatePublished - Jun 20 2003


  • Conditional gauge theorem
  • Conditional symmetric stable process
  • Green function

ASJC Scopus subject areas

  • Analysis


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