English

Complete monotonicity of time-changed L\'evy processes at first passage

Probability 2022-09-20 v2

Abstract

We consider the class of (possibly killed) spectrally positive L\'evy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following property: as functions of point of issue, the Laplace transforms of their first-passage times downwards are completely monotone. A wide (dense, in a sense) subfamily of this family admits closed form expressions for said Laplace transforms.

Keywords

Cite

@article{arxiv.2205.06654,
  title  = {Complete monotonicity of time-changed L\'evy processes at first passage},
  author = {Matija Vidmar},
  journal= {arXiv preprint arXiv:2205.06654},
  year   = {2022}
}