  We continue the investigation of the Levy processes on a q-deformed full Fock
space started in a previous paper. First, we show that the vacuum vector is
cyclic and separating for the algebra generated by such a process. Next, we
describe a chaotic representation property in terms of multiple integrals with
respect to diagonal measures, in the style of Nualart and Schoutens. We define
stochastic integration with respect to these processes, and calculate their
combinatorial stochastic measures. Finally, we show that they generate infinite
von Neumann algebras.
