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July 2004 Absolute continuity of symmetric Markov processes
Z.-Q. Chen, P. J. Fitzsimmons, M. Takeda, J. Ying, T.-S. Zhang
Ann. Probab. 32(3): 2067-2098 (July 2004). DOI: 10.1214/009117904000000432

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.

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Z.-Q. Chen. P. J. Fitzsimmons. M. Takeda. J. Ying. T.-S. Zhang. "Absolute continuity of symmetric Markov processes." Ann. Probab. 32 (3) 2067 - 2098, July 2004. https://doi.org/10.1214/009117904000000432

Information

Published: July 2004
First available in Project Euclid: 14 July 2004

zbMATH: 1053.60084
MathSciNet: MR2073186
Digital Object Identifier: 10.1214/009117904000000432

Subjects:
Primary: 31C25 , 60J45
Secondary: 60J57

Keywords: Absolute continuity , Dirichlet form , dual predictable projection , forward–backward martingale decomposition , Girsanov theorem , supermartingale multiplicative functional , symmetric Markov process

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 3 • July 2004
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