A stochastic Stinespring Theorem

Completely positive Markovian cocycles on a von Neumann algebra. adapted to a Fock filtration. are realised as conjugations of *-homomorphic Markovian cocycles. The conjugating processes are affiliated to the algebra. and are governed by quantum stochastic differential equations whose coefficients e volve according to the *-homomorphic process. Some perturbation theory for quantum stochastic flows: is developed in order to achieve the above Stines pring decomposition.