Volume 76, Number 6, December 2006
|Page(s)||1015 - 1021|
|Published online||29 November 2006|
Equivalence of the Markov chains and two-sided symbolic sequences
V. N. Karazin Kharkov National University - 4 Svoboda Sq., Kharkov 61077, Ukraine
2 A. Ya. Usikov Institute for Radiophysics and Electronics Ukrainian Academy of Science - 12 Proskura Street 61085 Kharkov, Ukraine
Corresponding author: firstname.lastname@example.org
Accepted: 31 October 2006
A new object of the probability theory, a two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory proposed in Phys. Rev. E, 68 (2003) 061107, is developed and used to establish the correspondence between these chains and two-sided sequences. The Markov chain is proved to be statistically equivalent to the definite two-sided one and vice versa. The results obtained for the binary chains are generalized to the chains of multi-valued symbols. Applicability of the two-sided chains to the examination of the one-dimensional Ising chains of classical spins is discussed.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ga – Markov processes / 87.10.+e – General theory and mathematical aspects
© EDP Sciences, 2006
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