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Right inverses of Levy processes: the excursion measure in the general case

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1.	Title	Title of document	Right inverses of Levy processes: the excursion measure in the general case
2.	Creator	Author's name, affiliation, country	Mladen Savov; University of Oxford
2.	Creator	Author's name, affiliation, country	Matthias Winkel; University of Oxford
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Levy process, right inverse, subordinator, fluctuation theory, excursion
3.	Subject	Subject classification	60G51
4.	Description	Abstract	This article is about right inverses of Lévy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	MS: supported by an Esmee Fairbairn Junior Research Fellowship at New College, Oxford
7.	Date	(YYYY-MM-DD)	2010-12-12
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1590
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1590
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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