We show that the general L\'{ e}vy 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 ${ \bf R}$. L\'{ e}vy's formula gives the most general cocycle possible.
Categories: math.PR math.FA