A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet (Q965085)

The authors give adequate extension, in the framework of a general Lévy process, of their previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The Lévy process framework allows to streamline their previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. The authors give some illustrations of the construction when the Lévy process is either a Gamma process or a Poisson process. The authors also work in the fractional Brownian and stable frameworks.