Periodic-orbit determination of dynamical correlations in stochastic processes.
It is shown that the large-deviation statistical quantities of the discrete-time, finite-state Markov process P_{n+1};{(j)}= summation _{k=1};{N}H_{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 coincide 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.
Kobayashi
Miki U
MU
Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. miki@acs.i.kyoto-u.ac.jp
Fujisaka
Hirokazu
H
Miyazaki
Syuji
S