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18 February 2021 Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin
Jacek Mucha
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Electron. J. Probab. 26: 1-33 (18 February 2021). DOI: 10.1214/21-EJP594

Abstract

We obtain an integral formula for the distribution of the first hitting time of the origin for one-dimensional α-stable processes , where . We also find a spectral-type integral formula for the transition operators of killed upon hitting the origin. Both expressions involve exponentially growing oscillating functions, which play a role of generalised eigenfunctions for .

Funding Statement

Work supported by National Science Centre (NCN), Poland, under grant 2015/19/B/ST1/01457

Citation

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Jacek Mucha. "Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin." Electron. J. Probab. 26 1 - 33, 18 February 2021. https://doi.org/10.1214/21-EJP594

Information

Received: 28 October 2019; Accepted: 30 January 2021; Published: 18 February 2021
First available in Project Euclid: 3 March 2021

Digital Object Identifier: 10.1214/21-EJP594

Subjects:
Primary: 60G51, 60G52
Secondary: 60J35, 60J45

JOURNAL ARTICLE
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Vol.26 • 2021
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