  Beyond the conventional quantum regression theorem, a general formula for
non-Markovian correlation functions of arbitrary system operators both in the
time- and frequency-domain is given. We approach the problem by transforming
the conventional time-nonlocal master equation into dispersed time-local
equations-of-motion. The validity of our approximations is discussed and we
find that the non-Markovian terms have to be included for short times. While
calculations of the density matrix at short times suffer from the initial value
problem, a correlation function has a well defined initial state. The resulting
formula for the non-Markovian correlation function has a simple structure and
is as convenient in its application as the conventional quantum regression
theorem for the Markovian case. For illustrations, we apply our method to
investigate the spectrum of the current fluctuations of interacting quantum
dots contacted with two electrodes. The corresponding non-Markovian
characteristics are demonstrated.
