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July, 1992 On the Distribution of the Hilbert Transform of the Local Time of a Symmetric Levy Process
P. J. Fitzsimmons, R. K. Getoor
Ann. Probab. 20(3): 1484-1497 (July, 1992). DOI: 10.1214/aop/1176989702

Abstract

We derive simple explicit formulas for the Fourier-Laplace transforms of the Hilbert transform and related functionals of the local time of a symmetric Levy process. These formulas generalize results of Biane and Yor for Brownian motion. The method of proof provides an explanation (of sorts) for the presence of the hyperbolic functions in such formulas.

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P. J. Fitzsimmons. R. K. Getoor. "On the Distribution of the Hilbert Transform of the Local Time of a Symmetric Levy Process." Ann. Probab. 20 (3) 1484 - 1497, July, 1992. https://doi.org/10.1214/aop/1176989702

Information

Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0767.60071
MathSciNet: MR1175273
Digital Object Identifier: 10.1214/aop/1176989702

Subjects:
Primary: 60J55
Secondary: 60J30

Keywords: Hilbert transform , Levy process , Local time

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 3 • July, 1992
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