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- W1587920249 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 $Esetminus F$. 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." @default.
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- W1587920249 date "2006-01-01" @default.
- W1587920249 modified "2023-09-25" @default.
- W1587920249 title "Entrance law, exit system and Lévy system of time changed processes" @default.
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- W1587920249 doi "https://doi.org/10.1215/ijm/1258059476" @default.
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