Absolute continuity of symmetric Markov processes

Z. Q. Chen; P. J. Fitzsimmons; M. Takeda; J. Ying; T. S. Zhang

doi:10.1214/009117904000000432

Absolute continuity of symmetric Markov processes

Z. Q. Chen^*
, P. J. Fitzsimmons
, M. Takeda
, J. Ying
, T. S. Zhang

^*Corresponding author for this work

University of Washington
University of California at San Diego
Tohoku University
Fudan University
University of Manchester

Research output: Contribution to journal › Article › peer-review

50 Citations (Scopus)

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	https://doi.org/10.1214/009117904000000432
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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10.1214/009117904000000432

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AU - Chen, Z. Q.

AU - Fitzsimmons, P. J.

AU - Takeda, M.

AU - Ying, J.

AU - Zhang, T. S.

PY - 2004/7

Y1 - 2004/7

N2 - 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.

AB - 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.

KW - Absolute continuity

KW - Dirichlet form

KW - Dual predictable projection

KW - Forward-backward martingale decomposition

KW - Girsanov theorem

KW - Supermartingale multiplicative functional

KW - Symmetric Markov process

UR - https://www.scopus.com/pages/publications/4544362747

U2 - 10.1214/009117904000000432

DO - 10.1214/009117904000000432

M3 - Article

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VL - 32

SP - 2067

EP - 2098

JO - Annals of Probability

JF - Annals of Probability

IS - 3 A

ER -

Absolute continuity of symmetric Markov processes

Abstract

Keywords

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