Absolute continuity of symmetric Markov processes

Z. Q. Chen, P. J. Fitzsimmons, M. Takeda, J. Ying, T. S. Zhang

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)

Abstract

We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of "gradient type." We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.

Original languageEnglish
Pages (from-to)2067-2098
Number of pages32
JournalAnnals of Probability
Volume32
Issue number3 A
DOIs
Publication statusPublished - 2004 Jul

Keywords

  • Absolute continuity
  • Dirichlet form
  • Dual predictable projection
  • Forward-backward martingale decomposition
  • Girsanov theorem
  • Supermartingale multiplicative functional
  • Symmetric Markov process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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