Periodic-orbit determination of dynamical correlations in stochastic processes

Miki U. Kobayashi, Hirokazu Fujisaka, Syuji Miyazaki

Research output: Contribution to journalArticlepeer-review


It is shown that the large-deviation statistical quantities of the discrete-time, finite-state Markov process P n+1 (j) = k=1 N Hjk Pn (k), where Pn (j) is the probability for the j state at the time step n and Hjk 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.

Original languageEnglish
Article number046205
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - 2007 Oct 4
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Periodic-orbit determination of dynamical correlations in stochastic processes'. Together they form a unique fingerprint.

Cite this