Absolute continuity of symmetric Markov processes

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.

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000432