Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2011-12-12
Physica D 240 (2011) 1370-1377
Nonlinear Sciences
Chaotic Dynamics
26 pages
Scientific paper
10.1016/j.physd.2011.05.019
We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [Amigo, J.M., Kennel, M. B., Kocarev, L., 2005. Physica D 210, 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.
Haruna Taichi
Nakajima Kohei
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