The area of a spectrally positive stable process stopped at zero
Probability
2014-10-02 v1
Abstract
An identity in law for the area of a spectrally positive L\'evy stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse Beta random variable and the square of a positive stable random variable. This identity entails that the stopped area is distributed as the perpetuity of a spectrally negative L\'evy process, and is hence self-decomposable. We also derive a convergent series representation for the density, whose behaviour at zero is shown to be Fr\'echet-like.
Keywords
Cite
@article{arxiv.1410.0036,
title = {The area of a spectrally positive stable process stopped at zero},
author = {Julien Letemplier and Thomas Simon},
journal= {arXiv preprint arXiv:1410.0036},
year = {2014}
}