A theory of systems with long-range correlations based on the consideration
of binary N-step Markov chains is developed. In the model, the conditional
probability that the i-th 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. A self-similarity of the studied stochastic process is revealed
and the similarity group transformation of the chain parameters is presented.
The diffusion Fokker-Planck equation governing the distribution function of the
L-words is explored. If the persistent correlations are not extremely strong,
the distribution function is shown to be the Gaussian with the variance being
nonlinearly dependent on L. The applicability of the developed theory to the
coarse-grained written and DNA texts is discussed.
Publié le : 2003-07-23
Classification:
Physics - Data Analysis, Statistics and Probability,
Condensed Matter - Statistical Mechanics,
Computer Science - Computation and Language,
Mathematical Physics,
Nonlinear Sciences - Adaptation and Self-Organizing Systems,
Physics - Classical Physics
@article{0307117,
author = {Usatenko, O. V. and Yampol'skii, V. A. and Kechedzhy, K. E. and Mel'nyk, S. S.},
title = {Symbolic stochastic dynamical systems viewed as binary N-step Markov
chains},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0307117}
}
Usatenko, O. V.; Yampol'skii, V. A.; Kechedzhy, K. E.; Mel'nyk, S. S. Symbolic stochastic dynamical systems viewed as binary N-step Markov
chains. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307117/