Fock Space Decomposition of Levy Processes
Abstract
We show that the general L\'evy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group, 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 R. L\'evy's formula gives the most general cocycle possible.
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