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Extensions of Lévy-Khintchine Formula and Beurling-Deny Formula in Semi-Dirichlet Forms Setting


Extensions of Lévy-Khintchine Formula and Beurling-Deny Formula in Semi-Dirichlet Forms Setting

Hu, Ze-Chun and 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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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 On:03 Jun 2010 20:03
Last Modified:04 Nov 2016 22:58


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