2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110504A 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.5 pagesData Analysis, Statistics and ProbabilityGeneral Physicstext