Existence of feller cocycles on a C*-algebra

The quantum stochastic differential equation dk_t = k_t o θ^α_β dΛ^β_α(t) is considered on a unital C*-algebra, with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for the existence of a completely positive contractive solution are shown to be sufficient. It is known that for completely positive contraction processes, k satisfies such an equation if and only if k is a regular Markovian cocycle. 'Feller' refers to an invariance condition analogous to probabilistic terminology if the algebra is thought of as a non-commutative topological space.