dorsal/arxiv
View SchemaSymbolic stochastic dynamical systems viewed as binary N-step Markov chains
| Authors | O. V. Usatenko, V. A. Yampol'skii, K. E. Kechedzhy, S. S. Mel'nyk |
|---|---|
| Categories | |
| ArXiv ID | physics/0307117 |
| URL | https://arxiv.org/abs/physics/0307117 |
| DOI | 10.1103/PhysRevE.68.061107 |
Abstract
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.
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"abstract": "A theory of systems with long-range correlations based on the consideration\nof binary N-step Markov chains is developed. In the model, the conditional\nprobability that the i-th symbol in the chain equals zero (or unity) is a\nlinear function of the number of unities among the preceding N symbols. The\ncorrelation and distribution functions as well as the variance of number of\nsymbols in the words of arbitrary length L are obtained analytically and\nnumerically. A self-similarity of the studied stochastic process is revealed\nand the similarity group transformation of the chain parameters is presented.\nThe diffusion Fokker-Planck equation governing the distribution function of the\nL-words is explored. If the persistent correlations are not extremely strong,\nthe distribution function is shown to be the Gaussian with the variance being\nnonlinearly dependent on L. The applicability of the developed theory to the\ncoarse-grained written and DNA texts is discussed.",
"arxiv_id": "physics/0307117",
"authors": [
"O. V. Usatenko",
"V. A. Yampol\u0027skii",
"K. E. Kechedzhy",
"S. S. Mel\u0027nyk"
],
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"physics.data-an",
"cond-mat.stat-mech",
"cs.CL",
"math-ph",
"math.MP",
"nlin.AO",
"physics.class-ph"
],
"doi": "10.1103/PhysRevE.68.061107",
"title": "Symbolic stochastic dynamical systems viewed as binary N-step Markov chains",
"url": "https://arxiv.org/abs/physics/0307117"
},
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