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On the density of exponential functionals of Levy processes
Levy processes exponential functional subordinators self-similar Markov processes
2011/9/14
Abstract: In this paper, we study the existence of the density associated to the exponential functional of the L\'evy process $\xi$, \[ I_{\ee_q}:=\int_0^{\ee_q} e^{\xi_s} \, \mathrm{d}s, \] where $\e...
Extended Factorizations of Exponential Functionals of Lévy Processes
Exponential functional Levy processes Wiener-Hopf factorizations Infinite divisibility Complete monotonicity
2011/8/24
Abstract: In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing...
Fluctuations of stable processes and exponential functionals of hypergeometric Levy processes
Hypergeometric L´ evy processes Lamperti-stable processes exponential functional
2011/1/18
We study the distribution and various properties of exponential functionals of hypergeometric
L´evy processes. We derive an explicit formula for the Mellin transform of the exponential function...
On the distribution of exponential functionals for Levy processes with jumps of rational transform
exponential functionals Levy processes rational transform
2010/11/22
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou o...
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Brownian motion Bessel process Lamperti's relation Hartman-Watson distributions
2009/5/18
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several rel...
Exponential functionals of Lévy processes
Lévy process exponential functional subordinator self-similar Markov process moment problem
2009/5/18
This text surveys properties and applications of the exponential functional $int_{0}^{t}exp(-xi_s)ds$ of real-valued Lévy processes $xi=(xi_t, tgeq0)$.