Absolute continuity of symmetric Markov processes
  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. 
Z.-Q. Chen, P. J. Fitzsimmons, M. Takeda, J. Ying and T.-S. Zhang