  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.

Probability;Functional Analysis