The time at which a Lévy process creeps

Details The time at which a Lévy process creeps The time at which a Lévy process creeps

2011-06-29

arxiv.org/abs/1106.5921v1

Electron. J. Probab. 16, 2182--2202 (2011)

Mathematics

Probability

Scientific paper

We show that if a L\'evy 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 $[0,\infty)$ and left differentiable on $(0,\infty)$, 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 $\rmd_H^{-1}$, 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 invers\'ee 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.

Affiliated with

Also associated with

No associations

Rating

The time at which a Lévy process creeps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The time at which a Lévy process creeps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The time at which a Lévy process creeps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-359284