Note, however, by the Ornstein isomorphism theorem, that every aperiodic and irreducible Markov chain is isomorphic to a Bernoulli scheme;Matthew Nicol and Karl Petersen, (2009) "Ergodic Theory: Basic Examples and Constructions", Encyclopedia of Complexity and Systems Science, Springer https://doi.org/10.1007/978-0-387-30440-3_177 thus, one might equally claim that Markov chains are a "special case" of Bernoulli schemes. The isomorphism generally requires a complicated recoding. The isomorphism theorem is even a bit stronger: it states that any stationary stochastic process is isomorphic to a Bernoulli scheme; the Markov chain is just one such example.
Note, however, by the Ornstein isomorphism theorem, that every aperiodic and irreducible Markov chain is isomorphic to a Bernoulli scheme;Matthew Nicol and Karl Petersen, (2009) "Ergodic Theory: Basic Examples and Constructions", Encyclopedia of Complexity and Systems Science, Springer https://doi.org/10.1007/978-0-387-30440-3_177 thus, one might equally claim that Markov chains are a "special case" of Bernoulli schemes. The isomorphism generally requires a complicated recoding. The isomorphism theorem is even a bit stronger: it states that any stationary stochastic process is isomorphic to a Bernoulli scheme; the Markov chain is just one such example.