On Girsanov and generalized Feynman-Kac transformations for symmetric processes

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	On Girsanov and generalized Feynman-Kac transformations for symmetric processes
	Chen, Chuan-Zhong ; Ma, Zhi-Ming; Sun, Wei
	2007-06-01
发表期刊	INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
ISSN	0219-0257
卷号	10 期号:2 页码:141-163
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.
关键词	symmetric Markov process Dirichlet form Girsanov transformation supermartingale generalized Feynman-Kac semigroup strong continuity
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical ; Statistics & Probability
WOS记录号	WOS:000250893800001
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5180
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.