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

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

47 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	2067-2098
页数	32
期刊	Annals of Probability
卷	32
期	3 A
DOI	https://doi.org/10.1214/009117904000000432
出版状态	已出版 - 7月 2004
已对外发布	是

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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

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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.",

keywords = "Absolute continuity, Dirichlet form, Dual predictable projection, Forward-backward martingale decomposition, Girsanov theorem, Supermartingale multiplicative functional, Symmetric Markov process",

author = "Chen, {Z. Q.} and Fitzsimmons, {P. J.} and M. Takeda and J. Ying and Zhang, {T. S.}",

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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

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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

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JO - Annals of Probability

JF - Annals of Probability

IS - 3 A

ER -

Absolute continuity of symmetric Markov processes

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