Mixing and observation for Markov operator cocycles*

We consider generalized definitions of mixing and exactness for random dynamical systems in terms Markov operator cocycles. first give six fundamental cocycles view observations the randomness environments, show that they can be reduced into two different groups. Secondly, we definition Lin's criterion naturally extended to case Finally, class asymptotically periodic cocycles, Lasota-Mackey type equivalence between mixing, asymptotic stability.