Splitting of Poisson Noise and Lévy Processes on Real Lie Algebras.

The compensated Poisson noise is expressed as a composite sum (splitting) of creation and annihilation operators, whose probabilistic interpretation relies on time changes. We construct an Itô table for this decomposition and obtain continuous and discrete time realizations of Lévy processes on the finite difference algebra fd and on sl[sub 2], e.g. the space-time dual of the Poisson process (compensated gamma process), and the continuous binomial process. [ABSTRACT FROM AUTHOR]