The Annals of Probability

On the Distribution of the Hilbert Transform of the Local Time of a Symmetric Levy Process

P. J. Fitzsimmons and R. K. Getoor

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 20, Number 3 (1992), 1484-1497.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989702

Digital Object Identifier
doi:10.1214/aop/1176989702

Mathematical Reviews number (MathSciNet)
MR1175273

Zentralblatt MATH identifier
0767.60071

JSTOR
links.jstor.org

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 60J30

Keywords
Levy process local time Hilbert transform

Citation

Fitzsimmons, P. J.; Getoor, R. K. On the Distribution of the Hilbert Transform of the Local Time of a Symmetric Levy Process. Ann. Probab. 20 (1992), no. 3, 1484--1497. doi:10.1214/aop/1176989702. https://projecteuclid.org/euclid.aop/1176989702


Export citation