The area of a spectrally positive stable process stopped at zero
DOI:
https://doi.org/10.19195/0208-4147.38.1.2Słowa kluczowe:
Hitting time, integrated process, stable Lévy process, tail asymptoticsAbstrakt
A multiplicative identity in law for the area of a spectrally positive Lévy ∝-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 simple identity makes it possible to study precisely the behaviour of the density at zero, which is Fréchet-like.
