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Extensions of Lévy–Khintchine formula and Beurling–Deny formula in semi-Dirichlet forms setting
- Source :
-
Journal of Functional Analysis . Oct2006, Vol. 239 Issue 1, p179-213. 35p. - Publication Year :
- 2006
-
Abstract
- Abstract: The Lévy–Khintchine formula or, more generally, Courrège''s theorem characterizes the infinitesimal generator of a Lévy process or a Feller process on . 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 Lévy–Khintchine and Beurling–Deny in semi-Dirichlet forms setting through introducing a quasi-compatible metric. [Copyright &y& Elsevier]
- Subjects :
- *DIRICHLET forms
*MATHEMATICAL forms
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 239
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 21913358
- Full Text :
- https://doi.org/10.1016/j.jfa.2005.12.015