A wide class of stochastic processes are described in
the non-Markovian Generalized Master Equations (GME) framework~[1]. Some
of them are
counting problems as the photon/electron counting in quantum
physics or the heat transport in thermal physics. Many
techniques was
developed assuming weak memory effects, the
Markovian approximation~[2], but outside of it the number of known
approaches dramatically drop.

Here we present a general theory to fully characterize the fluctuations
for a counting
problem even in the presence of non-Markovian effects.
We will make use of the concept of Full Counting Statistics (FCS) that
recently
has attracted intensive theoretical~[3,4] and experimental~[5] interest
in mesoscopic
transport. The FCS was demonstrated to be a sensitive diagnostic
tool in the detection of quantum-mechanical coherence, entanglement,
disorder,
and dissipation~[3].

Here we will generalize some the
techniques developed for the Markovian GME~[6,7] to the non-Markovian case.
For a short range in memory, no
power-law tails, we show some universal properties of cumulant
generating function
and how to calculate it~[8]. Beside we present a recursive method which
unifies, extending,
earlier approaches, making also possible an efficient numerical
treatment of complex
systems with many degrees of freedom~[9]. In the same framework we derive
the formula of the finite-frequency noise showing, in the presence of
memory, the
crucial role of the initial system-environment correlations.

As an illustrative example we apply the general scheme to calculate the
cumulants
and the finite frequency noise for the electron transport in a coherent
systems in
the presence of dissipation and decoherence.

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$[1]$ R.~Zwanzig, \textit{Nonequilibrium Statistical Mechanics}, Oxford
University
Press, 2001.\\
$[2]$ N.~G.~van~Kampen, \textit{Stochastic Processes in Physics and
Chemistry}, North
Hollad, 2007.\\
$[3]$ \textit{Quantum Noise}, ed. Yu.~V.~Nazarov, Kluwer, Dordrecht, 2003.\\
$[5]$ L.~S. Levitov, H. Lee, and G.~B. Lesovik, J. Math. Phys.,
\textbf{37}, 4845,
1996.\\
$[4]$ B.~Reulet, J.~Senzier, and D.~E. Prober, Phys. Rev. Lett.,
\textbf{91}, 196601,
2003; Yu.~Bomze, G.~Gershon, D.~Shovkun, L.~S. Levitov, and M.~Reznikov,
Phys. Rev.
Lett., \textbf{95}, 176601, 2005; T.~Fujisawa, T.~Hayashi, R.~Tomita,
and Y.~Hirayama,
Science, \textbf{312}, 1634,
2006.\\
$[6]$ D.~A. Bagrets and Yu.~V. Nazarov, Phys. Rev. B, \textbf{67},
085316, 2003.\\
$[7]$ C.~Flindt, T.~Novotn\'{y}, and A.-P. Jauho, Europhys. Lett.
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2005.\\
$[8]$ A.~Braggio, J.~K\"{o}nig, and R.~Fazio, Phys. Rev. Lett.
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2006.\\
$[9]$ C.~Flindt, T.~Novotn\'{y}, A.~Braggio, and A.-P. Jauho, Phys. Rev.
Lett.
\textbf{100}, 150601, 2008.