Estimates on the transition densities of Girsanov transforms of symmetric stable processes

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262-281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov transform introduced in Chen and Zhang [(2002), Ann. Inst. Henri poincaré 38, 475-505]. As an application of these results, we show that the Green function of Feynman-Kac type transforms of symmetric stable processes by continuous additive functionals of zero energy, when exists, is comparable to that of the symmetric stable process.

Original languageEnglish (US)
Pages (from-to)487-507
Number of pages21
JournalJournal of Theoretical Probability
Volume19
Issue number2
DOIs
StatePublished - Jun 2006

Keywords

  • Additive functionals of zero energy
  • Brownian motion
  • Dirichlet forms
  • Feynman-Kac semigroups
  • Girsanov transform
  • Green function
  • Martingale additive functionals
  • Symmetric Markov processes
  • Symmetric stable processes
  • Transition density

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Estimates on the transition densities of Girsanov transforms of symmetric stable processes'. Together they form a unique fingerprint.

Cite this