Abstract
A theory of systems with long-range correlations based on the consideration of binary -step Markov chains is developed. In our model, the conditional probability that the th symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length are obtained analytically and numerically. If the persistent correlations are not extremely strong, the variance is shown to be nonlinearly dependent on . 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.
- Received 14 November 2002
DOI:https://doi.org/10.1103/PhysRevLett.90.110601
©2003 American Physical Society