2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68105We show that the general Lévy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group, ${\bf R}$. The formula of de Finetti corresponds to coboundaries. Kolmogorov's processes correspond to cocycles of which the derivatives are cocycles of the Lie algebra of ${\bf R}$. Lévy's formula gives the most general cocycle possible.ProbabilityFunctional Analysis60G51text