  A finite quantum system S is coupled to a thermal, bosonic reservoir R.
Initial SR states are possibly correlated, obtained by applying a quantum
operation taken from a large class, to the uncoupled equilibrium state. We show
that the full system-reservoir dynamics is given by a markovian term plus a
correlation term, plus a remainder small in the coupling constant $\lambda$
uniformly for all times $t\ge 0$. The correlation term decays polynomially in
time, at a speed independent of $\lambda$. After this, the markovian term
becomes dominant, where the system evolves according to the completely
positive, trace-preserving semigroup generated by the Davies generator, while
the reservoir stays stationary in equilibrium. This shows that (a) after
initial SR correlations decay, the SR dynamics enters a regime where both the
Born and Markov approximations are valid, and (b) the reduced system dynamics
is markovian for all times, even for correlated SR initial states.
