Absolute Continuity

Absolute Continuity of Symmetric Markov Processes

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

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.

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June 11, 2002; revised April 11, 2003; re-revised July 25, 2003