  Stationary quantum stochastic process j is introduced as a *-homomorphism
embedding an involutive graded algebra $\tilde K=\oplus_{i=1}^{\infty}K_i$ into
a ring of (abelian) cohomologies of the one-parameter group $\alpha$ consisting
of *-automorphisms of certain operator algebra in a Hilbert space such that
every x from $K_i$ is translated into an additive $i-\alpha$-cocycle j(x). It
is shown that (noncommutative) multiplicative markovian cocycle defines a
perturbation of the stationary quantum stochastic process in the sense of such
definition. The $E_0$-semigroup $\tilde \beta$ on the von Neumann algebra $\cal
N$ associated with the markovian perturbation of K-flow j posseses the
restriction $\tilde \beta |_{{\cal N}_0}, {\cal N}_0\subset {\cal N}$, which is
conjugate to the flow of Powers shifts $\beta$ associated with j. It yields for
$\tilde \beta$ an analogue of the Wold decomposition for classical stochastic
process on completely nondeterministic and deterministic parts. The examples of
quantum stationary stochastic processes on the algebras of canonical
commutation, anticommutation and square of white noise relations are
considered. In the model situation of the space $L^2(\mathbb R)$ all markovian
cocycles of the group of shifts are described up to unitary equivalence of
perturbations.
