#### 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^{−1}_{H }, 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 Faculty Scholarship.* Paper 96.

http://surface.syr.edu/mat/96

#### 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