Hu, Ze-Chun, Ma, Zhe-Ming and Sun, Wei (2006) Extensions of Lévy-Khintchine Formula and Beurling-Deny Formula in Semi-Dirichlet Forms Setting. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
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Abstract
The Lévy-Khintchine formula or, more generally, Courrège’s theorem characterizes the infinitesimal generator of a Lévy process or a Feller process on Rd. 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.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Monograph (Technical Report) |
| Authors: | Hu, Ze-Chun and Ma, Zhe-Ming and Sun, Wei |
| Series Name: | Department of Mathematics & Statistics. Technical Report No. 1/06 |
| Corporate Authors: | Concordia University. Department of Mathematics & Statistics |
| Institution: | Concordia University |
| Date: | February 2006 |
| Keywords: | Lévy-Khintchine formula; Beurling-Deny formula; Quasi-regular semi-Dirichlet form; Local compactification; Integral representation; Quasi-compatible metric |
| ID Code: | 6671 |
| Deposited By: | DIANE MICHAUD |
| Deposited On: | 03 Jun 2010 20:03 |
| Last Modified: | 18 Jan 2018 17:29 |
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