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2021 The area under a spectrally positive stable excursion and other related processes
Christophe Profeta
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Electron. J. Probab. 26: 1-21 (2021). DOI: 10.1214/21-EJP618

Abstract

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.

Acknowledgments

We wish to thank the referees for pointing out some gaps in an earlier version of this manuscript.

Citation

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Christophe Profeta. "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

Information

Received: 5 September 2020; Accepted: 29 March 2021; Published: 2021
First available in Project Euclid: 3 May 2021

Digital Object Identifier: 10.1214/21-EJP618

Subjects:
Primary: 60E10, 60G18, 60G52

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Vol.26 • 2021
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