Isotropy Properties of the Multi-Step Markov Symbolic Sequences
  A new object of the probability theory, the two-sided chain of symbols (introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties of binary multi-step Markov chains with the long-range correlations. Established statistical correspondence between the Markov chains and certain two-sided sequences allows us to prove the isotropy properties of three classes of the Markov chains. One of them is the important class of weakly correlated additive Markov chains, which turned out to be equivalent to the additive two-sided sequences. 
S. S. Apostolov, Z. A. Mayzelis, O. V. Usatenko, and V. A. Yampol'skii