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 language | English |
|---|---|
| Pages (from-to) | 2067-2098 |
| Number of pages | 32 |
| Journal | Annals of Probability |
| Volume | 32 |
| Issue number | 3 A |
| DOIs | |
| Publication status | Published - Jul 2004 |
| Externally published | Yes |
Keywords
- Absolute continuity
- Dirichlet form
- Dual predictable projection
- Forward-backward martingale decomposition
- Girsanov theorem
- Supermartingale multiplicative functional
- Symmetric Markov process
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Chen, Z. Q., Fitzsimmons, P. J., Takeda, M., Ying, J., & Zhang, T. S. (2004). Absolute continuity of symmetric Markov processes. Annals of Probability, 32(3 A), 2067-2098. https://doi.org/10.1214/009117904000000432