Homomorphic Feller Cocycles on a C*-Algebra

When a Fock-adapted Feller cocycle on a C*-algebra is regular,completely positive and contractive, it possesses a stochasticgenerator that is necessarily completely bounded. Necessaryand sufficient conditions are given, in the form of a sequenceof identities, for a completely bounded map to generate a weaklymultiplicative cocycle. These are derived from a product formulafor iterated quantum stochastic integrals. Under two alternativeassumptions, one of which covers all previously considered cases,the first identity in the sequence is shown to imply the rest.