  It is shown that large deviation statistical quantities of the discrete time,
finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where
P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is
the transition probability, completely coincides with those from the Kalman map
corresponding to the above Markov process. Furthermore, it is demonstrated that
by using simple examples, time correlation functions in finite state Markov
processes can be well described in terms of unstable periodic orbits embedded
in the equivalent Kalman maps.
