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Extensions of Levy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting
Hu, Ze-Chun; Ma, Zhi-Ming; Sun, Wei
2006-10-01
Source PublicationJOURNAL OF FUNCTIONAL ANALYSIS
ISSN0022-1236
Volume239Issue:1Pages:179-213
AbstractThe Levy-Khintchine formula or, more generally, Courrege's theorem characterizes the infinitesimal generator of a Levy process or a Feller process on R-d. For more general Markov processes, the formula that comes closest to such a characterization is the Beurling-Deny formula for symmetric Dirichlet forms. In this paper, we extend these celebrated structure results to include a general right process on a metrizable Lusin space, which is supposed to be associated with a semi-Dirichlet form. We start with decomposing a regular semi-Dirichlet form into the diffusion, jumping and killing parts. Then, we develop a local compactification and an integral representation for quasi-regular semi-Dirichlet forms. Finally, we extend the formulae of Levy-Khintchine and Beurling-Deny in semi-Dirichlet forms setting through introducing a quasi-compatible metric. (C) 2006 Elsevier Inc. All rights reserved.
KeywordLevy-Khintchine formula Beurling-Deny formula quasi-regular semi-Dirichlet form local compactification integral representation quasi-compatible metric
DOI10.1016/j.jfa.2005.12.015
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000240748200008
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/3825
Collection应用数学研究所
Corresponding AuthorMa, Zhi-Ming
Affiliation1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
2.Sichuan Univ, Coll Math, Chengdu 610064, Peoples R China
3.Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China
4.Concordia Univ, Dept Math & Stat, Montreal, PQ H4B 1R6, Canada
Recommended Citation
GB/T 7714
Hu, Ze-Chun,Ma, Zhi-Ming,Sun, Wei. Extensions of Levy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2006,239(1):179-213.
APA Hu, Ze-Chun,Ma, Zhi-Ming,&Sun, Wei.(2006).Extensions of Levy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting.JOURNAL OF FUNCTIONAL ANALYSIS,239(1),179-213.
MLA Hu, Ze-Chun,et al."Extensions of Levy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting".JOURNAL OF FUNCTIONAL ANALYSIS 239.1(2006):179-213.
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