Inherent randomicity in 4-symbolic dynamics. (English) Zbl 1083.37502

Summary: The inherent randomicity in 4-symbolic dynamics is clarified in this paper. The symbolic sequences bear three characteristics. The distribution of frequency, inter-occurrence times and the alignment of two random sequences are amplified in detail. By using transfer probability of Markov chains, we obtain analytic expressions of generating functions in four probabilities stochastic wander models, which can be applied to all 4-symbolic systems. We hope to offer a symbolic platform that satisfies these stochastic properties and to study some properties of DNA sequences.


37B10 Symbolic dynamics
92D10 Genetics and epigenetics
37N25 Dynamical systems in biology
60C05 Combinatorial probability
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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