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2006 Entrance law, exit system and Lévy system of time changed processes
Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying
Illinois J. Math. 50(1-4): 269-312 (2006). DOI: 10.1215/ijm/1258059476

Abstract

Let $(X, \wh X)$ be a pair of Borel standard processes on a Lusin space $E$ that are in weak duality with respect to some $\sigma$-finite measure $m$ that has full support on $E$. Let $F$ be a finely closed subset of $E$. In this paper, we obtain the characterization of a L\'evy system of the time changed process of $X$ by a positive continuous additive functional (PCAF in abbreviation) of $X$ having support $F$, under the assumption that every $m$-semipolar set of $X$ is $m$-polar for $X$. The characterization of the L\'evy system is in terms of Feller measures, which are intrinsic quantities for the part process of $X$ killed upon leaving $E\setminus F$. Along the way, various relations between the entrance law, exit system, Feller measures and the distribution of the starting and ending point of excursions of $X$ away from $F$ are studied. We also show that the time changed process of $X$ is a special standard process having a weak dual and that the $\mu$-semipolar set of $Y$ is $\mu$-polar for $Y$, where $\mu$ is the Revuz measure for the PCAF used in the time change.

Citation

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Zhen-Qing Chen. Masatoshi Fukushima. Jiangang Ying. "Entrance law, exit system and Lévy system of time changed processes." Illinois J. Math. 50 (1-4) 269 - 312, 2006. https://doi.org/10.1215/ijm/1258059476

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1098.60076
MathSciNet: MR2247830
Digital Object Identifier: 10.1215/ijm/1258059476

Subjects:
Primary: 60J45
Secondary: 60J60

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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