Given a discrete time linear time varying system:

x(k+1) = A(k) * x(k) + B(k) * u(k)

Where A(k) and B(k) are generated by a stationary random process. Is there an equivalent linear time-invariant system which will calculate the expected trajectory of x(k)?

E[x(k+1)] = z(k+1) = Aeq * z(k) + Beq * u(k)

If so, how is it calculated?