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Cauchy's Principal Value of Local Times of Lévy Processes with no Negative Jumps via Continuous Branching Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Cauchy's Principal Value of Local Times of Lévy Processes with no Negative Jumps via Continuous Branching Processes
2.	Creator	Author's name, affiliation, country	Jean Bertoin; Université Paris VI
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Cauchy's principal value, Lévy process with no negative jumps, branching process.
3.	Subject	Subject classification	Primary: 60J30; secondary: 60F05, 60G10.
4.	Description	Abstract	Let $X$ be a recurrent Lévy process with no negative jumps and $n$ the measure of its excursions away from $0$. Using Lamperti's connection that links $X$ to a continuous state branching process, we determine the joint distribution under $n$ of the variables $C^+_T=\int_{0}^{T}{\bf 1}_{{X_s>0}}X_s^{-1}ds$ and $C^-_T=\int_{0}^{T}{\bf 1}_{{X_s<0}}|X_s|^{-1}ds$, where $T$ denotes the duration of the excursion. This provides a new insight on an identity of Fitzsimmons and Getoor on the Hilbert transform of the local times of $X$. Further results in the same vein are also discussed.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1997-09-01
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/20
10.	Identifier	Digital Object Identifier	10.1214/EJP.v2-20
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 2
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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