Distributional properties of exponential functionals of Lévy processes ∗

@inproceedings{Kuznetsov2012DistributionalPO,
title={Distributional properties of exponential functionals of L{\'e}vy processes ∗},
author={Alexey Kuznetsov and Juan Carlos Pardo and Mladen Savov},
year={2012}
}

We study the distribution of the exponential functional I(ξ, η) = ∫∞ 0 exp(ξt−)dηt, where ξ and η are independent Lévy processes. In the general setting, using the theory of Markov processes and Schwartz distributions, we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in [9]. In the special case when η is a Brownian motion with drift, we show that this integral equation leads to an important functional equation for the Mellin… CONTINUE READING