Fock Space Decomposition of Levy Processes

Details Fock Space Decomposition of Levy Processes Fock Space Decomposition of Levy Processes

2003-07-17

arxiv.org/abs/math/0307243v1

Mathematics

Probability

Scientific paper

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.

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