On Girsanov and generalized Feynman-Kac transformations for symmetric processes
文献类型：期刊论文
| 作者 | Chen, Chuan-Zhong; Ma, Zhi-Ming ; Sun, Wei
|
| 刊名 | INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
 |
| 出版日期 | 2007-06-01 |
| 卷号 | 10期号:2页码:141-163 |
| 关键词 | symmetric Markov process Dirichlet form Girsanov transformation supermartingale generalized Feynman-Kac semigroup strong continuity |
| ISSN号 | 0219-0257 |
| 英文摘要 | Let X be a Markov process, which is assumed to be associated with a symmetric Dirichlet form (epsilon, D(epsilon)). For u is an element of D(epsilon)(e), the extended Dirichlet space, we have the classical Fukushima's decomposition: (u) over tilde (X-t) - (u) over tilde (X-0) = M-t(u) + N-t(u), where (u) over tilde is a quasi-continuous version of u, M-t(u) the martingale part and N-t(u) the zero energy part. In this paper, we investigate two important transformations for X, the Girsanov transform induced by M-t(u) and the generalized Feynman-Kac transform induced by N-t(u). For the Girsanov transform, we present necessary and sufficient conditions for which to induce a positive supermartingale and hence to determine another Matkov process (X) over cap. Moreover, we characterize the symmetric Dirichlet form associated with the Girsanov transformed process (X) over cap. For the generalized Feynman-Kac transform, we give a necessary and sufficient condition for the generalized Feynman-Kac semigroup to be strongly continuous. |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000250893800001 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5179]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Chen, Chuan-Zhong |
| 作者单位 | 1.Hainan Normal Univ, Dept Math, Haikou 571158, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China 3.Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada |
| 推荐引用方式 GB/T 7714 | Chen, Chuan-Zhong,Ma, Zhi-Ming,Sun, Wei. On Girsanov and generalized Feynman-Kac transformations for symmetric processes[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,2007,10(2):141-163. |
| APA | Chen, Chuan-Zhong,Ma, Zhi-Ming,&Sun, Wei.(2007).On Girsanov and generalized Feynman-Kac transformations for symmetric processes.INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,10(2),141-163. |
| MLA | Chen, Chuan-Zhong,et al."On Girsanov and generalized Feynman-Kac transformations for symmetric processes".INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 10.2(2007):141-163. |
入库方式： OAI收割
来源：数学与系统科学研究院
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