On Marginal Markov Processes of Quantum Quadratic Stochastic Processes

In the paper it is defined two marginal Markov processes on von Neumann algebras $\text{cm}$ and $\text{cm}\text{o}\text{cm}$, respectively, corresponding to given quantum quadratic stochastic process (q.q.s.p.). It is proved that such marginal processes uniquely determines the q.q.s.p. Moreover, certain ergodic relations between them are established as well.