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Equivalence of Markov's Symbolic Sequences to Two-Sided Chains

S. S. Apostolov·Z. A. Mayzelis·O. V. Usatenko·V. A. Yampol'skii
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Abstract

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish the correspondence between these chains and two-sided ones. 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 taking on the arbitrary number of states.

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S. S. Apostolov, Z. A. Mayzelis, O. V. Usatenko, V. A. Yampol'skii. 2006-03-21. Equivalence of Markov's Symbolic Sequences to Two-Sided Chains. https://arxiv.org/abs/physics/0603172

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