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2012 Spectral theory for symmetric one-dimensional Lévy processes killed upon hitting the origin
Mateusz Kwaśnicki
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Electron. J. Probab. 17: 1-29 (2012). DOI: 10.1214/EJP.v17-2013

Abstract

Spectral theory for transition operators of one-dimensional symmetric Lévy process killed upon hitting the origin is studied. Under very mild assumptions, an integral-type formula for eigenfunctions is obtained, and eigenfunction expansion of transition operators and the generator is proved. As an application, and the primary motivation, integral fomulae for the transition density and the distribution of the hitting time of the origin are given in terms of the eigenfunctions.

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Mateusz Kwaśnicki. "Spectral theory for symmetric one-dimensional Lévy processes killed upon hitting the origin." Electron. J. Probab. 17 1 - 29, 2012. https://doi.org/10.1214/EJP.v17-2013

Information

Accepted: 1 October 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60045
MathSciNet: MR2988398
Digital Object Identifier: 10.1214/EJP.v17-2013

Subjects:
Primary: 60G51
Secondary: 60J45

JOURNAL ARTICLE
29 PAGES


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Vol.17 • 2012
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