On Markov perturbations of quantum random problems with stationary increments

We introduce “Markovian” cocycle perturbations of quantum stochastic processes with stationary increments and the Kolmogorov flows generated by them, which are characterized by a localization of the perturbation to the algebra of events of the past. The Markovian perturbations of the Kolmogorov flow generated by the quantum white noise result in the groups of automorphisms on the algebras of events (the von Neumann algebras in the quantum case) possessing the restrictions being isomorphic to the initial Kolmogorov flow. The possibility of obtaining this restriction can be interpreted as some analogue (in the quantum case) of the Wold decomposition, which allows us to exclude “nondeterministic” part of the process.