Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes

Abstract

In this paper we derive some distributional properties of Lévy processes and bridges from their cyclic exchangeability property. We first describe the ${\sigma}$-field which is invariant under the cyclic transformations. Then, by comditioning on this ${\sigma}$-field, we obtain some information about the laws of many functionals of Lévy processes and bridges, such as exponential functionals, quantiles and local time.