We study the distribution of the area under the normalized excursion of a spectrally positive stable Lévy process L, as well as the area under its meander, and under L conditioned to stay positive. Our results involve a special case of Wright’s function, which may be seen as a generalization of the classic Airy function appearing in similar Brownian’s areas.
We wish to thank the referees for pointing out some gaps in an earlier version of this manuscript.
"The area under a spectrally positive stable excursion and other related processes." Electron. J. Probab. 26 1 - 21, 2021. https://doi.org/10.1214/21-EJP618