Binary N-step Markov chains and long-range correlated systems.
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and numerically. If the persistent correlations are not extremely strong, the variance is shown to be nonlinearly dependent on L. A self-similarity of the studied stochastic process is revealed. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.
Usatenko
O V
OV
A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov, Ukraine.
Yampol'skii
V A
VA
D001412:Bacillus subtilis / Q000235:genetics; D004247:DNA / Q000235:genetics; D016680:Genome, Bacterial; D008390:Markov Chains; D008962:Models, Theoretical
D004247:DNA