Document Type

Article

Date

6-29-2011

Embargo Period

11-18-2011

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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1106.5921

Source

Harvested from arXiv.org

Creative Commons License


This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.