Periodic-orbit determination of dynamical correlations in stochastic processes

Details Periodic-orbit determination of dynamical correlations in stochastic processes Periodic-orbit determination of dynamical correlations in stochastic processes

2007-08-07

arxiv.org/abs/0708.0908v2

Nonlinear Sciences

Chaotic Dynamics

24 pages, 12 figures; added a comment on acceptance for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.76.046205

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.

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