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2018 Spectral analysis of stable processes on the positive half-line
Alexey Kuznetsov, Mateusz Kwaśnicki
Electron. J. Probab. 23: 1-29 (2018). DOI: 10.1214/18-EJP134

Abstract

We study the spectral expansion of the semigroup of a general stable process killed on the first exit from the positive half-line. Starting with the Wiener-Hopf factorization we obtain the q-resolvent density for the killed process, from which we derive the spectral expansion of the semigroup via the inverse Laplace transform. The eigenfunctions and co-eigenfunctions are given rather explicitly in terms of the double sine function and they give rise to a pair of integral transforms which generalize the classical Fourier sine transform. Our results provide the first explicit example of a spectral expansion of the semigroup of a non-symmetric Lévy process killed on the first exit from the positive half-line.

Citation

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Alexey Kuznetsov. Mateusz Kwaśnicki. "Spectral analysis of stable processes on the positive half-line." Electron. J. Probab. 23 1 - 29, 2018. https://doi.org/10.1214/18-EJP134

Information

Received: 13 December 2016; Accepted: 2 January 2018; Published: 2018
First available in Project Euclid: 12 February 2018

zbMATH: 1390.60173
MathSciNet: MR3771747
Digital Object Identifier: 10.1214/18-EJP134

Subjects:
Primary: 60G52, 60J35

JOURNAL ARTICLE
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Vol.23 • 2018
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