2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168977The one dimensional distribution of a Lévy process is not known in general even though its characteristic function is given by the famous Lévy-Khinchine theorem. This article gives an exact series representation for the one dimensional distribution of a Lévy process satisfying certain moment conditions. Moreover, this work clarifies an old result by Cramér on Edgeworth expansions for the distribution function of a Lévy process.Probability60G51text