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The Time at which a Lévy Process Creeps

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1.	Title	Title of document	The Time at which a Lévy Process Creeps
2.	Creator	Author's name, affiliation, country	Philip S Griffin; Syracuse University; United States
2.	Creator	Author's name, affiliation, country	Ross A Maller; Australian National University; Australia
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Lévy process, quintuple law, creeping by time $t$, second factorization identity, bivariate subordinator
3.	Subject	Subject classification	60G51; 60K05; 60G50.
4.	Description	Abstract	We show that if a Levy process creeps then the renewal function of the bivariate ascending ladder process satisfies certain continuity and differentiability properties. Then a left derivative of the renewal function is shown to be proportional to the distribution function of the time at which the process creeps over a given level, where the constant of proportionality is the reciprocal of the (positive) drift of the ascending ladder height process. This allows us to add the term due to creeping in the recent quintuple law of Doney and Kyprianou (2006). As an application, we derive a Laplace transform identity which generalises the second factorization identity. We also relate Doney and Kyprianou's extension of Vigon's equation amicale inversee to creeping. Some results concerning the ladder process, including the second factorization identity, continue to hold for a general bivariate subordinator, and are given in this generality.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Research partially supported by ARC Grant DP1092502.
7.	Date	(YYYY-MM-DD)	2011-11-13
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/945
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-945
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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