English

Potentials of stable processes

Probability 2021-01-22 v1

Abstract

For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum. The results are obtained by exploiting a simple connection with the Lamperti representation and exit problems of stable processes.

Keywords

Cite

@article{arxiv.1312.1222,
  title  = {Potentials of stable processes},
  author = {A. E. Kyprianou and A. R. Watson},
  journal= {arXiv preprint arXiv:1312.1222},
  year   = {2021}
}

Comments

10 pages

R2 v1 2026-06-22T02:20:47.059Z