Document Type
Article
Date
6-30-2011
Disciplines
Mathematics
Description/Abstract
We show that if a Levy process creeps then, as a function of u, the renewal function V (t, u) of the bivariate ascending ladder process (L−1,H) is absolutely continuous on [0,∞) and left differentiable on (0,∞), and the left derivative at u is proportional to the (improper) distribution function of the time at which the process creeps over level u, where the constant of proportionality is d−1H, the reciprocal of the (positive) drift of H. This yields the (missing) 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 of X, including the second factorization identity, continue to hold for a general bivariate subordinator, and are given in this generality.
Recommended Citation
Griffin, Philip S. and Maller, Ross A., "The Time at Which a Lévy Process Creeps" (2011). Mathematics - All Scholarship. 101.
https://surface.syr.edu/mat/101
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1106.5921